Energy Levels of Light Nuclei A = 15
|
|
- Κανδάκη Βαμβακάς
- 6 χρόνια πριν
- Προβολές:
Transcript
1 Revised Manuscript 4 August 08 Energy Levels of Light Nuclei A = F. Ajzenberg-Selove University of Pennsylvania, Philadelphia, Pennsylvania Abstract: An evaluation of A = was published in Nuclear Physics A (970), p.. This version of A = differs from the published version in that we have corrected some errors discovered after the article went to press. Figures and introductory tables have been omitted from this manuscript. Reference key numbers have been changed to the NNDC/TUNL format. (References closed December, 969) The original work of Fay Ajzenberg-Selove was supported by the US Department of Energy [DE-AC0-76-ER078]. Later modification by the TUNL Data Evaluation group was supported by the US Department of Energy, Office of High Energy and Nuclear Physics, under: Contract No. DEFG0-88-ER4044 (North Carolina State University); Contract No. DEFG0-9-ER4069 (Duke University).
2 Nucl. Phys. A (970) A = Table of Contents for A = Below is a list of links for items found within the PDF document. Figures from this evaluation have been scanned in and are available on this website or via the link below. A. Nuclides: B, C, N, O, F B. Tables of Recommended Level Energies: Table.: Energy levels of C Table.4: Energy levels of N Table.8: Energy levels of O C. References D. Figures: C, N, O, Isobar diagram E. Erratum to this Publication: PS or PDF
3 B B has been identified in the. GeV proton bombardment of uranium. It is particle stable (966PO09). See also (960ZE0, 96BAC, 966GA). GENERAL: C (Figs. 9 and ) See (960TAC, 96TAE, 964LIB, 964STB, 967LO0). See also (969AR).. C(β ) N Q m = 9.77 The half-life is. ± 0.0 sec (96DO7),.49 ± 0.07 sec (964NE09). The β-spectrum is complex. Transitions have been observed both to the ground state and to the upper of the. MeV levels of N: the latter transition is clearly allowed: see Table. (99AL06, 966AL, 969GA0). The ground state transition of N*(.) has E γ =.990± MeV (967CH9); J π for this state is (see Table.4). Thus J π ( C) = or (99AL06, 964AL: see also (96WA0)). See also (96KIB, 968ZHB) and N.. 9 Be( 6 He, α) Be Q m = 6.4 E b = Be was irradiated with 4 MeV neutrons and the decay of Be was observed [ 9 Be(n, α) 6 He, followed by the above reaction]: the cross section (which is determined for a large 6 He energy spread) is ± 0 mb (967ST).. 9 Be( 7 Li, p) C Q m = 9.09 Observed proton groups are listed in Table. (97MU99, 964CA0). τ m for C*(0.7) is (.77 ± 0.) nsec (968ME08: delayed coincidence technique). Angular distributions of the protons to C*(0, 0.7) are reported at E( 7 Li) =.6,.8, 6.0, 6. MeV by (969SN0) C(d, p) C Q m =.006
4 Table.: Energy levels of C E x (MeV ± kev) J π ; T τ Decay Reactions g.s. ; τ / =. ± 0.08 sec β,, ± 7 ; τ m =.76 ± 0.0 nsec γ, 4 (.48 ± 0).08 ± 40, 4 4. ± 0, 4 (4.60).9 ± 0, ± 0, ± 40 (6.84) (7.06) 7. ± 0, 4 (7.69) (8.00) 8. ± 60 (8.47) Table.: Beta decay of C (99AL06, 966AL, 969GA0) Decay to N* J π Branch (%) log ft a log ft b (MeV) (exp) (theor) g.s ,,, 9.0, a Using τ m =. ± 0.0 sec. b See (99AL97). ±.96 ± ± 4.04 ± (0.8 ± 0.) ± (.0 ± 0.6) 0.06 ± (. ± 0.) 0.99 ±
5 Table.: Proton groups from 9 Be( 7 Li, p) C and 4 C(d, p) C E x (MeV ± kev) E x (MeV) (97MU99) (99MOB) (964CA0) c ± 60 a 0.7 ± ± 0 b.08 ± ± ± ± ± a (97NO4) reports E x = 0.70 ± 0.0 MeV. b Not observed by (964CA0). c ±0 kev (private communication) Identification of C g.s. with N*(.6), T =, Jπ =, is suggested by (96BA6). At E d = 4.9 MeV, proton groups are observed to the ground state of C and to the levels at 0.7,.09, 4.,.94, 6.8 and 7. MeV (±0 kev) (99MOB). The angular distribution of ground state protons implies l n = 0, J π = (99MOB: see also (96PUB) and ref. 9 there, (964AL)); for the first excited state, l n =. θ = 0.09 and 0.0 (99MOB), 0.6 and 0.06 (966GL0) for the ground state and the first excited state, respectively. See also (967NE06). The 0.7 MeV level has a mean life of.7 ± 0. nsec (96LO0); E γ = 70 ± 7 kev. The angular distribution of the γ-rays requires J. Since the l n = stripping requires J π = or, J π = is established (96CH4). The observed lifetime excludes J > (96LO0). See also (964NE09, 96WA0, 966AL, 967CH9).
6 . 4 C(n, γ) C Q m =.8 The capture cross section is < µb (9YAA) O(n, α) C Q m =.009 See (966BAF). The following reactions leading to C have not been reported: C(t, p) C Q m = C(t, d) C Q m =.09 4 C(α, He) C Q m = 9.60 N(n, p) C Q m =
7 N (Figs. 0 and ) GENERAL: Model calculations: (97HAE, 99BRE, 99FEB, 960TAC, 96BAE, 96BUC, 96KUB, 964MAG, 96CO, 96FAB, 96GRH, 96GUA, 96ZAB, 966EL08, 966SO0, 967CO, 967EL0, 967PA0, 968ELA, 968HOH, 968MAB, 968SH08, 968WA04, 968ZH0, 969CHR, 969ELB). General calculations and reviews: (964EVA, 96BEB, 966OLC, 966WIE, 967FAA, 967LO0, 968BIC, 968ZHB, 969HAG, 969IWB). Electromagnetic transitions: (96RON, 966HA, 966PO, 966ROP, 966ROU, 966WAE, 967KUE, 967POJ, 967WAC, 968BIC, 968SH08, 968YAE, 968ZH06, 968ZHB, 969KHC, 969ZHA). Meson interactions: (969KAR). Other: (96BA0, 964VAD). Ground state: µ = nm (96BA6, 964LI4, 967COD). See also (96BR, 964STB, 96ICA, 96MAT, 966MAV, 966WIE, 967SH4, 968PE6, 968ROE, 969CHR, 969FU).. (a) 9 Be( 6 Li, p) 4 B Q m =.0 E b =.9 (b) 9 Be( 6 Li, α) B Q m = 4.47 (c) 9 Be( 6 Li, n) N Q m =.9 (d) 9 Be( 6 Li, 8 Be) 7 Li Q m =.87 (e) 9 Be( 6 Li, He) 0 B Q m =.9 The yield of p 0 and p (reaction (a)) for E( 6 Li) =.84 to 6.40 MeV shows some broad structure: analysis in terms of Ericson fluctuation theory gives a value of 0.4 MeV for the average level width at E x = 8 MeV in N (967SE08). The excitation functions for α 0, α and α (reaction (b)) [E( 6 Li) = to 4 MeV: (96LE0)] and the yield of N (reaction (c)) [E( 6 Li) =. to. MeV: (96NO0)] show a smooth increase in the cross section with energy. For reactions (d) and (e) see (96MC). See also (96BAQ).. 9 Be( 7 Li, n) N Q m =
8 At E( 7 Li) =.9 MeV, γ-rays are observed which are assigned to the ground state decay of N*(9.0, 9.8, 0.80) (964CA8). See also (97NO7). Table.4: Energy levels of N a E x (MeV ± kev) J π ; T τ m (psec) or Γ (kev) Decay Reactions 0.70 ± ± ± ± ± ± 8.6 ± ± 9.0 ± 9.8 ± 0. stable,, 4, 8, 9, 0,,, 4,,,, 4,, 6, 9, 0,, 9, 40, 4, 4, 4, 44, 4, 46, 49, 0,,,, 4,, 6, 7, 8, 9, 60, 6, 6, 6, 64, 6, 66 τ m =.9 ± 0. γ, 4, 8,,,,,, 6, 9, 0,, 9, 4,,,, 8, 9, 6 < 0.0 γ, 4, 8,,,,,, 6, 9, 0,, 9, 46,,,, 8, 9 < γ, 4, 8, 0,,,,, 6, 9, 0,, 9, 49,,,, 7, 8, 9, 6 < 0.08 γ, 4, 8,,,, 6, 9,, 9,,, 6 < 0.0 γ, 4, 8,,,, 6, 9,, 9, 46,,,, ± 0.0 γ, 4, 8,,,,, 9, 9,,, 6 < 0.00 γ, 4, 8,, 6, 9,, 9, 46,,,, 6 γ, 4, 8,,,, 6,, 9,,, 6 γ,, 4, 8,, 6, 9,, 9, 46, γ, 4, 8,,,, 9,, 9,, 9.49 ± 0. ( ) < 0.00 γ, 4, 8,,,, 9,, 9,, 9. ±. or b < 0. γ, 9, 9, 9.76 ±. γ, 9,, ± < 0.9 γ,, 4, 8,,, 9,, 9.99 ± 4 (, ) γ, 9 8
9 Table.4: Energy levels of N a (continued) E x (MeV ± kev) J π ; T τ m (psec) or Γ (kev) Decay Reactions ± γ,, 9,, 0.4 ± 7 γ, p,, 6, 9 () 0.6 ± γ, p, 6, ± () ± (0.94 ± 0).6 ± Γ =. n.94 ±.48 ±.6 ± 4 γ, p,, 6, 7, 9, γ, p,, 4, 8,,, 6, ± 0. γ, n, p 6, 7, 8,, 4.4 ±. γ, n, p, α, 6, 7, 8,, ; ± 6. γ, n, p 6, 7, ± 40 ± n, p, α, 8,,.877 ± ± 4 n, p, α, 8,,,.94 ± 6 ( 9 ) n,,.96 ±.097 ± 4.4 ±.6 ± 4.49 ± 4 () ; ;. ± 0.9 ± ± 0 ( 7 ± n, p, α, 8,, 4 ± γ, n, p, α, 6, 7, 8,,, 8 47 ± 7 γ, n, p, α, 6, 7, 8,,, 9 n, p, 8,, 4 γ, n, p, α, 6, 8,,, 8, 80 p 7, 67 ± 8 n, p, α, 6, 8,,, 8 0 p, α 6 ).4 < n, p, α, 6, n, p, α, 6, 8, ± 8 n, p, α, 6, 8, n, p, α 6, 8, (.) n, p 8.60 (, 7 ) ± 4 n, p, α, 6, 8,,, n, p, α 6, n, p, α,, 8.7 n, α n, p, α 8,, 8.89 n, α 9
10 Table.4: Energy levels of N a (continued) E x (MeV ± kev) J π ; T τ m (psec) or Γ (kev) Decay Reactions 4.0 p, α n, α 4. 0 n, p, α, 8,, 8, () ± n, p, α, 8,, n, α 4. n, α n, p, α,, p, α n, p ± n, p, α,, n, p, α, n, p n, p, α, 8, 8.00 n, p, α, 8. n, p, α, 8, 8,.9 n, α.7 n, t, α,. n, α 8.6 n, α.74 p, t, α.8 < n, p, t, α, 6,.89 ± 0 < n, t, α,.96 ± 0 n, t, α,.99 n, α 6.0 n, p, t, α, 6,, n, p, t, α, 6,, ± 40 n, p, t, α, 6, 6.9 n, p, t, α, 6, 6. ± 0 n, p, t, α, 6,, ± 0 n, p, t, α, 6,, ± 0 n, p, d, t, α, 6,, ± 70 n, p, t, α, 6,, ± 0 00 n, p, d, t, α, 6,,, 6,, 8 0
11 Table.4: Energy levels of N a (continued) E x (MeV ± kev) J π ; T τ m (psec) or Γ (kev) Decay Reactions 6.74 n, p, α, ± 0 n, p, d, t, α, 6,,, ± 0 t, α n, p, d, t, α, 6,,,, n, p, α, 6,, p, t 7.0 broad d, t, α, ± 0 n, p, t, α, 6, 7.9 n, p, α, 6, n, p, α, 6, 8, n, p, d, t, α, 6,, 6, 8, n, p, α, 6, n, p, α, ± n, p, d, t, α, 6, ± 0 00 n, d, α, ± 0 48 ± 9 (p), d, t, α 6, 8, n, α, n, p, α, ± 0 9 ± 4 (n), d, α, ± 0 4 (n), p, d, t, 6, n, α ± 0 0 ± 60 n, p, d, α, 6, 9, ± 0 0 n, d 9. γ, p γ, p 48.7 γ, p γ, p 48 a See also Tables.7 and.0. See (967PH0).. 0 B( 6 Li, p) N Q m = 8.7
12 Table.: Resonances in B α E α (MeV) Γ lab (kev) Particle out E x (MeV) J π Refs. a 0.60 n.4 (94BE08) b.0 n.7 (94BE08).8 n.86 (94BE08).0 n.9 (94BE08). n, p.0 (9SH46).8 n, p. (9SH46) n 0, p n 0, p 0.9 (9SH46, 96BO6, 98HAB, 99LE8) (96BO6, 98HAB, 99LE8, 96MA8, 966MA04) p 0.9 (99LE8, 96MA8).94 < 6 n 0, p 0. (96BO6, 98HAB, 99LE8).99 8 n 0, p 0.8 (96BO6, 98HAB, 99LE8, 966MA04). 9 n 0, p.6 (96BO6, 98HAB, 99LE8, 96MA8, 966MA04). 40 p.4 (99LE8, 96MA8).6 0 n 0, p.6 (, 7 ) (96BO6, 98HAB, 99LE8, 96MA8, 966MA04).64 0 p 0.66 (96MA8).7 40 n 0.7 (96BO6, 98HAB, 96MA8, 966MA04).76 n 0.7 (966MA04).9 n 0.89 (96MA8, 966MA04) 4. p (96MA8) 4.9 n 4.06 (96MA8, 966MA04) 4.4 n (96MA8, 966MA04) 4. n 4. (96BO6, 98HAB, 96MA8, 966MA04) 4. n (96MA8, 966MA04) 4.4 n 0 4. (96MA8, 966MA04) 4.6 p 0 (4.) (96MA8)
13 Table.: Energy levels of N a (continued) E α (MeV) Γ lab (kev) Particle out E x (MeV) J π Refs. a p (96MA8) n (96BO6, 98HAB).4 n (98HAB).49 n 0.0 (98HAB).8 n 0.08 (98HAB).86 n 0.9 (98HAB).98 n 0, n.7 (98HAB) 6.0 n 0, (n ).6 (98HAB) 6.60 n, p.8 (96ED0) c 6.7 n 0, (n ).9 (98HAB) 6.74 n 0, n.9 (98HAB) 6.8 n 0, n.99 (98HAB) 6.89 n, p 6.04 (98HAB, 96ED0) 6.94 n, p 6.08 (96ED0) 7.08 n, p 6.8 (96ED0) 7.6 n, p 6. (96ED0) 7. n, p 6. (96ED0) 7.4 n, p 6.4 (96ED0) 7.6 n, p 6. (96ED0) 7.6 n, p 6.60 (96ED0) 7.77 n, p 6.69 (96ED0) 7.84 n, p 6.74 (96ED0) 7.86 n, p 6.7 (96ED0) 8.07 n, p 6.9 (96ED0) 8.7 n, p 6.98 (96ED0)
14 Table.: Energy levels of N a (continued) E α (MeV) Γ lab (kev) Particle out E x (MeV) J π Refs. a 8.44 n, p 7.8 (96ED0) 8.46 n, p 7.9 (96ED0) 8.9 n, p 7.9 (96ED0) 8.68 n, p 7. (96ED0) 8.88 n, p 7.0 (96ED0) 8.96 n, p 7.6 (96ED0) 8.99 n, p 7.8 (96ED0) 9.49 n, p 7.9 (96ED0) a It should be noted that (94BE08), (98HAB) and (96ED0) are unpublished. They are quoted here only because of the dearth of 4 published information on these resonances. b And private communication. c Resonant energies listed by (96ED0) are ±40 kev.
15 At E( 6 Li) = 4.9 MeV, thirty proton groups are observed corresponding to N states with E x < 6.8 MeV. Angular distributions have been measured for the proton groups corresponding to N*(.7.0, 6., , 7.7, 8., 8.8, ) (966MC0). The ground-state γ-decay of N*(9.8, 0.80) is reported by (964CA8). See also (96MOB) B( 7 Li, d) N Q m =.7 At E( 7 Li) =. MeV, thirty deuteron groups are observed corresponding to N states with E x <. MeV. Angular distributions have been measured for the deuteron groups corresponding to N*(0,.7.0, 6., , 7.7, 8., 8.8, , 9.8) (966MC0). See also (96MOB). The ground state γ-decay of N*(8., 9.0, 9.8, 0.80) is reported by (964CA8).. B(α, n) 4 N Q m = 0.7 E b = 0.99 Reported resonances are displayed in Table. (94BE08, 9SH46, 96BO6, 98HAB, 96ED0, 96MA8, 966MA04). See also (96GOJ, 96GOJ, 96TSA) and (966WEB). See also 4 N. 6. B(α, p) 4 C Q m = E b = 0.99 Reported resonances are listed in Table. (9SH46, 99LE8, 96ED0, 96MA8). Partial widths for several resonances are listed by (99LE8, 96MA8). See also 4 C. 7. B(α, d) C Q m =.68 E b = 0.99 The yield of ground state deuterons has been measured for E α = 7 to MeV by (967AL6). See also C. 8. (a) B( 6 Li, d) N Q m = 9.0 (b) B( 7 Li, t) N Q m = 8. At E( 6 Li) = 4.7 MeV and at E( 7 Li) =.00 MeV, angular distributions are reported for the deuterons and the tritons corresponding to N*(0,.7.0, 6., , 7.7, 8., 8.8, ) (966MC0). See also (96MOB). Gamma rays are observed in reaction (a) which are assigned to the ground state transitions of N*(9., 9.8, 0.80) (964CA8). See also (96HOE) and (964HA09).
16 9. B( 9 Be, He) N Q m = See (96HOE). 0. B( 6 O, C) N Q m =.8 At E( 6 O) = 7, 0,. and MeV, angular distributions corresponding to transitions to N*(0, 6.) have been measured by (96BO4, 966BO): the ground state angular distributions show strong diffraction structure. See also (969GOR, 969BRD, 969KAG).. (a) C(t, n) 4 N Q m = 4.0 E b = 4.80 (b) C(t, p) 4 C Q m = 4.64 (c) C(t, t) C (d) C(t, α) B Q m =.88 Reported resonances are listed in Table.6 (96VA, 96GU0, 96KU09, 96NI04, 96SE0, 969ET0). The triton yield has been measured for E t = 9 to MeV by (96GL04). See also (96NED, 964GRH, 967CH), B and C in (968AJ0), and 4 C and 4 N.. C(α, p) N Q m = 4.96 Angular distributions of the protons corresponding to the ground state transition have been measured at E α =.4 to 6.0 MeV (967IVB), 6. to 9.0 MeV (960PR), 9.7 to. MeV (96YAC), 0.6 to. MeV (96KO04), to 9 MeV (99NO8) and at 4 MeV (96LI07). Angular distributions are also reported for the groups to N*(.7.0, 6., ) (99NO8: 4.6 MeV) and N*(6.) (96LI07: 4 MeV). See also (96EI0, 969GLD), (96KRA, 96HOD, 96TEB, 96DAB, 964DAD, 964KEC, 96NED, 966HIC, 967ROK; theor.) and (99AJ76).. C( 7 Li, α) N Q m =.8 Angular distributions have been measured at E( 7 Li) =. to 4.0 MeV (96HO06; α 0, α, α ) and 0. MeV (969GL07; α 0, α, α and the α s corresponding to N*(7., 7.6, 8.6, 9., 0., 0.9,.8,.,.). (969BAU) report the excitation of N*(.,., 4.9,.6, 6., 6.8, 8.9, 9.8) and (969GL07) also report α groups corresponding to N*(.8, 6.) 6
17 Table.6: Resonances in C t E t (MeV ± kev) E x (MeV) Particles out Refs α 0 (96NI04, 969ET0)..74 p 0, t 0, α (96GU0, 96KU09, 96NI04, 969ET0)..8 t 0 (969ET0).0 ± 0.89 n, α 0 (96VA, 969ET0).9 ± 0.96 n, t 0, α 0 (96VA, 969ET0) p 0 (969ET0) n, α 0, α (96VA, 969ET0).6 ± n, α 0 (96VA, 96SE0, 969ET0) α 0 (969ET0).8 ± 0 6. n, p 0, α 0, α (96VA, 96SE0, 969ET0).98 ± n, p 0 (96VA, 969ET0).0 ± p 0, t 0, α 0 (96SE0, 969ET0).8 ± 6.9 n, p 0, t 0, α 0, α (96VA, 969ET0).8 ± n, p 0, α 0, α (96VA, 96SE0, 969ET0).9 ± n, t 0, α 0, α (96VA, 96SE0, 969ET0).0 ± α 0, α (96SE0, 969ET0) α 0 (969ET0) p 0 (969ET0) t 0, α 0, α (969ET0).89 ± α 0 (96SE0, 969ET0) α (969ET0) and, possibly N*(7., 8.). The mean lifetime of N*(9.8) <.9 0 sec (see Table.7): E γ = 46.6 ± 4.0 kev ( N*(9.8.7)) (969TH0). See also (960SH0) and (969GIB, 969ROG). 4. (a) C( 4 N, C) N Q m = 7.88 (b) C( 9 F, 6 O) N Q m =.0 For reaction (a) see (969BRD); for reaction (b) see (969ROG).. C(d, n) 4 N Q m =. E b =
18 Table.7: Lifetimes of some N states E x (MeV) τ m (psec) Reaction Refs..7 > 6 O(t, α) (96AL9) 9 Be( 4 N, 8 Be) (969NI09).9 ± 0. 4 N(d, p) (967BI).0 < C(p, γ) (968COZV) (4. ±.8) 0 4 N(d, p) (96AL9) (. ± 0.7) 0 4 N(n, γ) (969WE07) 6. < N(d, p) (968GI) < N(n, γ) (969WE07) < C(p, γ) (968COZV) 7.6 < N(d, p) (968GI) 0. ± 0.0 C( He, p) (966LI07) 0.00 ± C(p, γ) (968COZV) 7.0 < N(d, p) (968GI) < N(n, γ) (969WE07) < C(p, γ) (968COZV) ± 0.0 C( He, p) (966LI07) 0.06 ± N(d, p) (968GI) 8. < N(d, p) (968GI) < N(n, γ) (969WE07) < C(p, γ) (968COZV) 9. < C(p, γ) (968COZV) < N(n, γ) (969WE07) 9. < 0. 6 O(γ, p) (969MU07) 9.8 < 0.9 C( 7 Li, α) (969TH0) 8
19 Table.8: Resonances in C d E d (MeV) Emitted particles Γ lab (kev) N* (MeV) Refs. 0.7 p 6.47 (96VA7) 0.64 n, p (90CU, 90RI7, 9KO4, 96MA46, 96VA7) 0.8 n (90RI7).0 α 0 broad 7. (96MA, 966KL06).4 ± 0.04 t (96MA).40 ± 0.04 p 0, t 0, α (96MA, 96MA46). a n 00 (94BEA, 90RI7, 966KL06).64 ± 0.04 t (96MA).78 ± 0.0 n, α (90RI7, 9MA76, 96MA).80 ± 0.0 (p 0 ), t 0, α ± (96MA, 96MA46).0 ± 0.0 (n), α 0, α ± (96MA, 96AL). ± 0.0 (n), p 0, t (96MA, 96MA46, 96AL).4 ± 0.0 n, p 0, α 0 70 ± (9MA76, 96MA, 96MA46).46 ± 0.0 n (9MA76, 96DE9) a Possibly to be identified with.40 MeV resonance (96MA). Observed resonances are displayed in Table.8 (90RI7, 9MA76, 96AL, 96DE9). Excitation functions have recently been measured for E d = 0.8 to. MeV (96JA09; n 0, n, n, n, n ),.0 to. MeV (96AL: 7.0 MeV γ-ray) and. to 4.0 MeV (96DE9; n 0 ). See also (960VA). Polarization measurements are reported for E d =. to 4.0 MeV (967MEN; n 0, n, n ) and.8 MeV (96GAG; n, n 4, n ). See also 4 N. 6. C(d, p) 4 C Q m =.9 E b = 6.60 Observed resonances are displayed in Table.8 (94BEA, 90CU, 9KO4, 96MA46). Excitation functions have recently been measured for E d = to.4 MeV (968LIL; p 0, p ),.0 to 4.0 MeV (96LA09: 4 C*(6.09, 6.7, 7.4)),. to 4. MeV (96DE9; p 0 ), and 4. to 6. MeV (968CO04; p ). See also (96AL). See also 4 C. 7. C(d, d) C E b =
20 Excitation functions for elastically scattered deuterons have been measured for E d = to.4 MeV (968LIL) and 4. to.7 MeV (968CO04). 8. C(d, t) C Q m =. E b = 6.60 Observed resonances are listed in Table.8 (96MA). (968LIL) report measurement of the t 0 excitation function for E d = to.4 MeV. A polarization study has been made at E d =. MeV (969DEH; t 0, t ). See also C. 9. C(d, α) B Q m =.68 E b = 6.60 Observed resonances are listed in Table.8 (96MA). See also (966KL06, 966KLF, 968CO04, 968LIL). 0. C(t, n) N Q m = 9.90 Not reported.. C( He, p) N Q m = Observed proton groups and γ-rays corresponding to N states are listed in Table.9 (99YO, 966GA08, 966WA08, 967PH0). Gamma-ray branching ratios obtained by (96WA6, 966PE04, 966WA08) are displayed in Table.0 which also shows J π values obtained from angular correlation measurements. The two states at E x = 9.6 MeV [see reactions and 9] are separated by. ± 0. kev (968ST0). See also (99BR79). The τ m for N*(7.6, 7.7) are 0. ± 0.0 psec and 0. ± 0.0 psec, respectively: see Table.7 (966LI07). Angular distributions of the ground state protons have been measured for E( He) = 8.7 to 0.9 MeV (96AL0). See also (99AJ76). See also (967YOC, 968WE), (96CLA, 966PRB) and 6 O in (97AJ0).. C(α, d) N Q m = This reaction has been studied at E α = 40. MeV: see Table.9 (969LU07). 0
21 Table.9: Energy levels in N from C( He, p) N and C(α, d) N E x (MeV ± kev) a (99YO) (966GA08) (966WA08) b (967PH0) (969LU07) c.8 ±.66 ± 0 6. ± 6.6 ± ± 7.70 ± ± 7.77 ± 7.8 ± ± 8. ± ± ± ± ± ± ± ± ± 9.69 ± 0 9. ± 6 9. ± ± 9.87 ± ± ± ± ± ± ± ± ± ± ± ± (0.94 ± 0) d a See also (96SH, 966GOJ, 966PHB). b E γ, except for E x = 0.94 MeV; errors for E γ are nominal. c C(α, d) N: E α = 40. MeV. d (969LU07) also reports levels at E x =.90 ± 0.00 (J π = ( 9 )),.8 ± 0.00 and.08 ± 0.00 MeV (J π = ( )).
22 Table.0: Radiative decays in N E i (MeV) J π i E f (MeV) J π f Branch (%) Refs (96WA6, 966PE04, 969SI04) < (96WA6) < (966PE04) < (966PE04) < (96WA6) < (96WA6) < (969SI04) < (968GI) < 4 (966HA0) 00 (96WA6, 966PE04, 968GI) > 97 (969SI04) < 9 (967TH0) < 4 (966AL8) < 4 (968GI) < (966PE04) (967TH0) < 0. (96WA6) 00 (966PE04, 969SI04) 98 ± (96WA6, 968GI) ± (96WA6) <. (968GI) ± (968GI) < (966PE04) < 0. (96WA6) < (96WA6) < 4 (966HA0) < (966PE04) 00 (96WA6, 966PE04, 968GI) < (96WA6) < 4 (966AL8) < 6 (968GI)
23 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs < 0.6 (96WA6) 80 ± (96WA6) 77 ± (966WA08) 70 ± 4 (966PE04) 79. ±.9 (967PH0) < (96WA6).0 0 ± (96WA6).7.0 ± (966WA08) c.7 ± (966PE04) 0.9 ±. (967PH0) 7.8 ± (96WA6) ± (966PE04) 4.4 ±.0 (967PH0) < (96WA6) 6 (966PE04). ± 0.6 (967PH0). ± 0.4 (96WA6) 4.4 ± 0.7 (967PH0) 4 ± 4 (96WA6) ± (966WA08) 7 ± 4 (966PE04).4 ±.0 (967PH0) 6 ± 4 (96WA6) 6 ± (966WA08).0 < (96WA6) ± 4 (966PE04) ±.0 (967PH0) ± (96WA6) 7 (966PE04).4 ± 0.6 (967PH0) < (96WA6) < 4 (966WA08).6 ± 0. (967PH0)
24 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs a < 0.7 (96WA6) < (966WA08) < (96WA6, 966WA08) 9 ± (96WA6) 9 ± 4 (966WA08) 9.6 ± 0.9 (967PH0).8 ± (96WA6). ± (966WA08) 4.7 ± 0.7 (967PH0) ± (96WA6) 4. ± (966WA08).7 ± 0. (967PH0) < 0 (96WA6). ± 0.4 (96WA6) < (96WA6) < (967PH0) 0 9. a ( ) 0 < 0. (96WA6) 97 (968ST0) 00 (969SI04).7.0 (968ST06) (968ST0) 7 (967TH0) 8 (967TH0).0 0 (967TH0) (968ST0) (969SI04) 8 (968ST0) 9 (969SI04) 0 (967TH0) 44 (968ST0) 8 (969SI04) 4 (967TH0) 7 9 (968ST0) 4
25 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs < 0 (96WA6) 4. ±. (967PH0) < (96WA6) ±.7 (967PH0) (96WA6) (96WA6) 4.7 ±. (967PH0) < 0 (96WA6) < (967PH0) < 0 (96WA6).6 ± 0.7 (967PH0) < 0 (96WA6) < (967PH0) 0 < (96WA6) 00 (96WA6) 8. ±.8 (967PH0).7.0 < 0 (96WA6) ±. (967PH0) < (96WA6).7 ± 0.8 (967PH0) < 0 (96WA6). ± 0. (967PH0) < (96WA6) < (967PH0) < 0 (96WA6).0 ± 0.6 (967PH0) < (96WA6) < (967PH0) < (96WA6) < (967PH0) < 0 (96WA6) < 4 (967PH0) 00 (96WA6)
26 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs..0 < (96WA6) ±.8 (967PH0) (, ) < (96WA6). ± 0.9 (967PH0) < 0 (96WA6).4 ±. (967PH0) < 0 (96WA6).7 ± 0.9 (967PH0) < 0 (96WA6) 7. ±.0 (967PH0) < (967PH0) 80 ± 0 (96WA6) 77.6 ±.9 (967PH0) ± 0 (96WA6) ±. (967PH0) 0 ± 0 (96WA6) 4.9 ±. (967PH0) < 0 (96WA6) < (967PH0) < (96WA6). ± 0.8 (967PH0) < 0 (96WA6) < (96WA6) 8.8 < (96WA6) 7.7, 8., 8.8 < (967PH0) 0 00 (96WA6) 96.0 ± 0.7 (967PH0) 94 ± 4 (966WA08).7.0 < 0 (96WA6) ± 0.7 (967PH0) 6 ± (966WA08) < (96WA6) < (966WA08) 6
27 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs b < 7 (96WA6) < (966WA08) < (96WA6) < (966WA08) < 7 (96WA6) < (966WA08) < (96WA6) < (96WA6) ± (96WA6) < 4 (966WA08, 967PH0) ± 8 (96WA6) ± (966WA08) 6.4 ±.4 (967PH0) ± 8 (96WA6) 8 ± (966WA08) 4.7 ±.6 (967PH0) < 0 (96WA6) < 6 (966WA08) 4 ± 4 (96WA6) < 6 (966WA08) < 0 (96WA6) < 6 (966WA08). ± 0. (967PH0) 9.0 < (967PH0) ± 0. (967PH0) ± 0.7 (967PH0) ±. (967PH0) 9.9 (, ).7 ±. (967PH0) < 4 (967PH0) ± 0. (969SI04) 0 ± (969SI04) 7 ± 0. (969SI04) ±. (969SI04) 7
28 Table.0: Radiative decays in N (continued) E i (MeV) J π i E f (MeV) J π f Branch (%) Refs (9.) (9.) ±. (969SI04).8 ± 0.4 (969SI04) < (969SI04) ± (969SI04) 8 ± (969SI04) 6 ± 0.4 (969SI04) < (969SI04) ± 0. (969SI04) < (969SI04) < (969SI04) < (969SI04) ± (96WA6) ± (966WA08) 47 ± (969SI04) ± 0. (969SI04).0 ± 0.6 (969SI04) ± (96WA6) ( 47 ± (966WA08) < (96WA6) < 0 (966WA08) 7 ± 0. (969SI04) < (96WA6) 9 ± 0. (969SI04) < (96WA6) < 4 (966WA08) 8 ± 0. (969SI04) < 7 (96WA6) ± 0. (969SI04) ± 0. (969SI04) ± 0. (969SI04) ) 4 ± 0. (969SI04) a See also (96WA6, 967PH0). b See also (960HE). c See also (969SI04). 8
29 . C( 6 Li, α) N Q m = Angular distributions have been measured for E( 6 Li) =. to.8 MeV for the α 0 and α groups (964BLB). 4. C( 7 Li, He) N Q m = See (969TH0).. C( B, 9 Be) N Q m = 0.4 See (966POE, 967POE, 967VOA) C(p, γ) N Q m = 0.08 Resonances for capture γ-radiation are listed in Table. (99FEC, 99HED, 968HE, 968SIF, 969SI04). A combination of N*(0.80) and (9.8) permits a good account of the low energy (n, n) and (n, γ) cross sections (99HED). The thermal (n, p) cross section can be ascribed to the E p =. MeV resonance ( N*(.6)) (9BA44: see also 4 N(n, γ) N). See also (99AJ76) and (969TI0). Table.0 displays branching ratios obtained in this and in other reactions. The angular distributions of γ-rays at the E p = 0. MeV resonance ( N*(0.4)) leads to assignments of J =, ( ), and, respectively, for N*(.7, 7.6, 7.0, 0.4) (960HE). The angular distribution of the (0.8 8.) γ-ray fixes J = for N*(8.) (968SIE). A triple correlation study by (968SIE) of the decay of N*(0.80) to the E x = 9. MeV states suggests J = for the upper and J = for the lower of these two states. Lifetimes for various N states have been measured by (968COZV): see Table.7. See also (960FR09, 96FRD, 969ZHA) C(p, p) 4 C E b =
30 Table.: Resonances in 4 C p a 0 E p Γ Γ n Γ p Γ γ J π d E x Refs. (MeV ± kev) (kev) (kev) (kev) (ev) (MeV) 0.6 ± a 0.4 (99HED, 968SIF, 969SI04) 0. ± a (.4 ± 0.4) 0 c 0.6 (99HED, 960HE, 968SIF, 969SI04) 0.7 ± a ± 0. c (99HED, 968SIF, 969SI04) 0.64 ± a 0. ± 0.04 c (99HED, 968SIF, 969SI04).6 ± 7.9 ± (9RO6, 9BA44, 96SA06, 968HA7).94 ± 4 4 ± 4.6. e (968HA7).88 ± ±. 4.6 ± ± ± (9RO6, 9BA44, 96SA06, 968HA7) e.47 ± 8 48 ± (968HA7).09 ± ± ± ± ± 0.4 ; T =.6 (99FEC, 968HE).688 ± (9RO6, 9BA44, 96SA06).788 ± , ( ).876 (9RO6, 9BA44, 96SA06).884 ± (9RO6, 9BA44, 96SA06).0 ± 4 b 4 ± (9RO6, 9BA44, 96SA06, 960BA4, 968HA7).077 ± b 47 ± (9RO6, 9BA44, 96SA06, 960BA4, 968HA7, 968HE) ().7 ± (9RO6, 9BA44, 96SA06, 960BA4, 968HA7).40 ± 4 b ; T =.49 (9RO6, 96SA06, 960BA4).48 ± ; T =. (968HA7, 968HE).908 ± (96SA06, 960BA4, 96HA, 96HA0).9..9 (960BA4, 96HA, 96HA0).8.6 (960BA4, 96HA, 96HA0)
31 Table.: Resonances in 4 C p a (continued) E p Γ Γ n Γ p Γ γ J π d E x Refs. (MeV ± kev) (kev) (kev) (kev) (ev) (MeV) (960BA4, 96HA, 96HA0). (.) (96HA0).6.60 (960BA4, 96HA, 96HA0).7.67 (96HA, 96HA0) (960BA4, 96HA, 96HA0) (960BA4, 96HA, 96HA0) (960BA4, 96HA, 96HA0) (960BA4, 96HA, 96HA0) (960BA4, 96HA) (96HA, 96HA0).4.00 (96HA, 96HA0).6. (96HA, 96HA0) a See also (99HEB) and Table. in (99AJ76). b The Γ α are < 0. kev for E res =.6 to. MeV, except for the resonances at E p =.0,.08 and.4 MeV for which they are, respectively, 0.6,. and. kev (96SA06). c ωγ (in ev) (968SIF, 969SI04). d See also (99AJ76). e These states correspond to the levels listed in the line below: a different boundary condition was used to obtain E res.
32 The elastic scattering has been studied for E p = 0.4 to.7 MeV. At the E p = 7 kev resonance (see Table.), the scattering is consistent with d-wave formation of a J π = state. No anomalies are observed at E p = 0. and 0.6 MeV (99HED). However, anomalies are observed at E p =.6,.9,.47,.0,.07 and.48 MeV: the parameters of these are displayed in Table. (968HA7, 968HE). The.48 MeV anomaly is due to a J π = ; T = state at E x =. MeV (which is the analog to the first excited state of C), and is distinct from the J π = resonance in 4 C(p, n) 4 N observed at E p =.4 MeV (968HE). See also (968IWA, 969IWE) C(p, n) 4 N Q m = 0.66 E b = 0.08 Resonances reported by (9RO6, 9BA44, 96SA06, 99FEC, 960BA4, 96HA, 96HA0, 968HE) are listed in Table.. In addition to these, (96HA) report (in an abstract) a broad resonance corresponding to a T = state of N at E x =.6 MeV. At E p =.79 MeV, the distributions favor, but is not excluded (9BA44: see also (9KA0)); a computation of the cross section favors J = (96SA06). At E p =.88 MeV, the angular distribution is consistent with the J π = assignment from 4 N(n, n) 4 N (9BA44). The E p =.7 MeV state has J = or ; the σ nn clearly indicates ther latter (9BA44, 96SA06). For N*(.6) (E p =. MeV), the proton reduced width indicates a single-particle level, while the neutron reduced width is only 0. This is consistent with the assignment T =, corresponding to the ground state of C (9BA44, 96BA6, 99FEC). See also (967VOB, 969BAN, 969TI0). Polarization measurements are reported at E p = 7., 8.8 and 0.4 MeV by (969WOJ; n 0, n, n ) C(d, n) N Q m = Angular distributions have been determined at E d =.,.8 and.8 MeV (967COR; n 0, n, n, n 46 ),. to.08 MeV (96IM0; n 0 ),.0 and. MeV (96IM0; n, n, n 46 ) and.0 MeV (967LA; n 0, n, n, n 4, n, n 6 and N*(8., 9.06, 9.6, 9.)). The transitions to N*(.0, 9.06) involve l p = 0: these states therefore have J π = (967LA). See also (99AJ76) and (96CH4, 964MOG). Studies of the γ-decay of N states reached in this and in other reactions are summarized in Table.0: see (96WA6). See also (967CH9) C( He, d) N Q m = 4.7
33 At E( He) = 4 MeV, angular distributions of the deuterons corresponding to N*(0,.8,.0, 6.) have been measured and analyzed by DWBA: the relative spectroscopic factors for the first four states of N are, 0.0, 0.4, 0.07 in good agreement with the predictions of (97HAE). Angular distributions of the d 0 group are also reported at E( He) = 9 MeV by (96WE, 966DUB, 968DAN).. 4 C(α, t) N Q m = Not reported.. 4 N(n, γ) N Q m = 0.8 Q 0 = 0.8 ± (968GR4). The thermal cross section is 80 ± 0 mb (97BA8), 7 ± 7. mb (964ST). This large cross section is not understood in terms of the present level structure in N: see (99AJ76). Observed capture γ rays are displayed in Table. (96MOC, 967TH0, 968GR4). The very accurate γ-ray energy determinations of (968GR4) show that two states at E x 9. MeV are involved in this reaction as previously suggested by (966WA08). The lower of the two, at E x = 9.8 MeV, decays predominantly to the ground state. The other state at E x = 9.49 MeV, which is preferentially fed in this reaction, decays primarily by cascades via N*(.7,.0, 6., 7.6) (968GR4). See also reactions and 9, (968GRZY, 968ST0) and Table.0. Recoil Doppler broadening of cascade γ-rays has been measured by (969WE07): the derived τ m are listed in Table.7. See also (968CAJ). Observation of non-isotropic correlations in the C 6. cascade means that J for N*(6.): the results are consistent with J = (964BA0). The importance of measuring the (n, γ) cross section at E n = 0.47 and 0.66 MeV for astrophysical considerations is suggested by (968FOA). See also (960CA0, 96JA09, 969HOX) and (98GR0, 964LIC).. 4 N(n, n) 4 N E b = 0.8 The thermal (bound) scattering cross section is. b (96WIA). The scattering amplitude (bound) is a = 9.9±0. fm (96DO4) [a = 9.4±0.0 fm is recommended by (964ST)]. See also (969BAP). The coherent scattering cross section is 0. ± 0. b (964ST). Recent cross section measurements are listed in Table.. Cross section data are summarized in (964ST), while angular distribution data are displayed in (96GOM). Observed resonances are listed in Table.4 (9JO, 9HI, 9FO7, 99HA, 966FOD, 966FOE, 966MAK, 968BO6, 968JOF): for a discussion of the evidence
34 Table.: Gamma radiation from 4 N(n, γ) N Transition in N E γ (MeV ± kev) E γ (MeV ± kev) I γ b (967TH0) (968GR4) (968GR4) (967TH0) (96MOC) C ± ± 0.6. ±.0 4 C.7.6 ±.6 ± ± 0. C.0.4 ±. ± ± 0.9 C ± ± ± C ±.6777 ± 0..9 ± 0.8 < C 7.0. ±. ± ± 0. 9 C 8.. ±.0 ± ± 0. 6 C ± ± 9. ± 0. C ± ± 0. d ±.69 ± ± ± ±.978 ± ± 0..4 ± ± 6.0 ± ± ± ± ±.8848 ± ± ± 0.8 ± ± ± ± ± ± 8.0 ± ± ± ±. ± ± ± 4 c 0. ± ± ± 4 c 0. ± ± ± ± ± 0..7 ± ±.887 ± ± ±.8 ± 0..0 ± ±.8 ± 0..0 ± ±.9996 ± ± 0. 4 a C = capturing state. b In units of photons/00 captures. c (967TH0). d (968GR4). 4
35 leading to J π assignments, see (99AJ76). See also (960BA4) and (966AGA, 967BEF, 968IWA, 969IWE). A polarization measurement has been made at E n =. MeV by (96OT0). See also (96TA07) N(n, n) N Q m = 0. E b = 0.8 Table.: Recent cross section measurements for 4 N n a E n (MeV) Measurements of Refs σ t (99BI9) σ t (960BA4).0 4. σ t (966MAK, 968JOF) σ ne (968BO6) σ e (968BO6) 4., 6, 7 σ nn γ (968COW) σ nn γ (969DIB) σ t, σ e, σ ne (967BA0). 9. σ e (968BO6) 4 σ e (96BA46) σ ne (969NYA)., 9.8 σ ne (96DEG). σ t, σ ne (968HAV) σ t (960PE) 88 σ t (966ME4) 0 7 σ n,n (96BRA). 8 σ n,n (960FE). 8.8 σ n,n (96BO4).. σ n,n (960MC0) 4. σ n,n (96CEB) 4.4 σ n,n (96RA06) 4.7 σ n,n (967PA7) 4.8 σ n,n (96GR4). 4. σ n,p (99GA4)
36 Table.: Recent cross section measurements for 4 N n a (continued) E n (MeV) Measurements of Refs σ n,p (969DIB) 4.7 σ n,p, σ n,np (966CSB, 967CS0) σ n,p, σ n,d (969NYA) σ n,t (966SC).7 8. σ n,t (99GA4) 4. σ n,α (967MO) σ n,t (969NYA).7 σ n,t (967MO). 8. σ n,α (99GA4) σ n,α (966SC) σ n,α (968COW).7 8. σ n,α (99HA) σ n,α (969DIB) 4.7 σ n,α (966CSB) σ n,α (969NYA) a See also (99AJ76). Recent measurements of cross sections for this reaction are listed in Table. (960FE, 960MC0, 96BRA, 96RA06, 96CEB, 96BO4, 96GR4, 967PA7): see the summaries in (964ST, 966JEB). See also (964HE8, 966CSC, 967CS0) and (99AJ76).. 4 N(n, p) 4 C Q m = 0.66 E b = 0.8 The thermal cross-section is.8 ± 0.0 b (964ST),.8 ± 0.0 b (96HA4). A number of resonances are reported by (90JO7), (99GA4) and (96EN0): see Table.4. The results are summarized in (964ST, 966JEB). See also (960BUC, 968DAF). Recent cross-section measurements are listed in Table. (99GA4, 966CSB, 967CS0, 969DIB). See also (964FOA, 969BAN) and (99AJ76). 6. (a) 4 N(n, d) C Q m =. E b = 0.8 (b) 4 N(n, np) C Q m = 7.0 For reaction (a) see (967LI06) and (99AJ76). For reaction (b) see (966CSB, 967CS0). 6
37 Table.4: Resonances in 4 N n a 7 E res (MeV ± kev) Γ lab (kev) Γ n (kev) Γ p (kev) Γ α (kev) J π N* (MeV) Refs ±. < < (9JO, 9HI) ± < < ± ± (90JO7, 9HI, 96EN0).4 (90JO7, 9JO, 9HI).766 (90JO7, 9JO, 9HI).0 ± ± 6. < < (9HI). ± ± ± () () ().880 (9JO, 9HI, 9FO7).96 (9HI).094 (9JO, 9HI, 9FO7, 99GA4).4 (90JO7, 9JO, 9HI, 9FO7, 99GA4).9 ± 8 0. < ± ( ).494 (90JO7, 9HI, 9FO7, 99GA4, 966FOE). (9HI, 9FO7, 99GA4, 966FOD, 966FOE) (99GA4, 966FOD, 966FOE, 966MAK, 968JOF).47 < r.4 (99GA4). 7 r.9 (99GA4).7 40 r.74 9 r.6 (99GA4).9 (99GA4) r r.7 (99GA4).9 (99GA4, 966FOE, 966MAK, 968JOF). 8 r r.8 (99GA4, 966FOE, 966MAK, 968JOF). 0 r r 4. (99GA4).7 0 r r 4.7 (99GA4, 966MAK, 968JOF) (99GA4) r r 4.6 (99GA4, 966SC) r r 4.7 (99GA4) r 4.9 (99GA4, 966SC) 4.60 r. (99GA4, 966SC).0 r. (99GA4, 966SC, 968BO6) r 6.06 (99GA4, 966SC, 968BO6) ()
38 Table.4: Resonances in 4 N n a (continued) E res (MeV ± kev) Γ lab (kev) Γ n (kev) Γ p (kev) Γ α (kev) J π N* (MeV) Refs..94 r 6.8 (99GA4, 966SC) r 6.8 (99GA4, 966SC) r r 6.67 (99GA4, 99HA, 966SC) r r 6.9 (99GA4, 99HA) 6.94 r 7. (99GA4) 00 r (99HA) 7.6 r 7. (99GA4) r 7.68 (99GA4) r r 7.8 (99GA4, 99HA) r 8. (99HA) r 8.0 (99GA4, 99HA) 8 r = resonant channel. a See also (99AJ76).
39 7. (a) 4 N(n, t) C Q m = 4.0 E b = 0.8 (b) 4 N(n, t) 4 He 4 He 4 He Q m =.89 (c) 4 N(n, α) 7 Li Q m = 8.8 For reaction (a) see (99GA4, 966SC, 967LI06, 967RE0) and (968AJ0). For reaction (b) see (967MO). For reaction (c) see (967MO). See also (960FA0, 964SAE), Table., the summaries in (964ST, 966JEB) and (99AJ76). 8. (a) 4 N(n, α) B Q m = 0.7 E b = 0.8 (b) 4 N(n, nα) 0 B Q m =.6 Recent cross-section measurements for reaction (a) are displayed in Table.: these include measurements of cross sections for several different α-groups (99GA4, 966SC) and γ-rays (99HA, 968COW, 969DIB). For summaries of the experimental evidence, see (964ST, 966JEB). Observed resonances are listed in Table.4 (90JO7, 99GA4, 966SC). See also (960FA0), (960BUC, 96CHC) and (964GAA, 968GAM; theor.). For reaction (b), see (960FA0) N(d, p) N Q m = 8.60 Q 0 = 8.64 ± (964MA7). Proton groups corresponding to levels of N are listed in Table. (90MA6, 94SP0, 96DO4, 96AL9, 966GA08, 966GOJ, 969PH0). The J π assignments are based on PWBA and DWBA analyses: see (99AJ76), (969PH0) and Table.6 for a listing of recent angular distribution studies in the range E d = 0. to 7 MeV. See also (966ROV). The angular distributions of protons corresponding to N*(6.) and the p-γ angular correlation fixes J π = for that state (96GO0). (960HOB) has looked for additional states of N with E x 7 MeV: he finds the upper limits to proton groups corresponding to 7.0 < E x < 7. to be %, and to be % of the intensities of groups to known nearby states for 7. < E x < 7.7 MeV. Recent very accurate γ-ray energy measurements have been reported by (967CH9) [E γ = 99.0 ± 0.4 and ± 0.46 kev] by (966AL8) and by (96WA6): the derived E x values are displayed in Table.. Branching ratios have been determined by (96WA6, 968GI, 968ST0) and are shown in Table.0 together with the multipolarities determined by (96WA6). Lifetime measurements are listed in Table.7 (96AL9, 967BI, 968GI). The two states of N at E x = 9. MeV [see Table.0 for branching ratios] are separated by. ± 0. kev (968ST0, 969YOC): see also reaction. 9
40 Table.: N levels from 4 N(d, p) N 40 E x (MeV ± kev) l n J π (90MA6, 966GOJ) (94SP0) (96DO4, 967CH9) A (966GA08) 0 b.76 ± 6.80 ± 0.79 ± 0.46 a.7 ± 0 c 7.0 ± ± 0.4 a.00 ± c,d 6.8 ± ± 0 e,i 7.64 ± ± 0 7. ±.7 f,i ± ± ± 8 0 f,i 7.7 ± ± ±.0 g,i 7 8. ± ± ± ± 4. 0 e,i 8.7 ± ± ±. 8.8 ± 0 h,i ± ± 9.6 ± ± 6 i,, 9. ± ± 6 or i ( ) 9.76 ± ± ± ± ± ± ± ± 6, 0 i 0.48 ± ± ± ± ± ± 7, 0 i 0.8 ± ± 9 i. j j,,,,,,
41 A: (96AL9, 96WA6, 966AL8). a See also (96AL9, 96WA0). b (9GI0, 97WA0). c (9SH8: see (98WAC)). d Isotropic: no clear stripping pattern. e (9GI0, 9SH8, 96GR7, 98WAC). f (9SH8, 96GR7). g (96GR7): (97WA0) find a possible l = 0 component. h (9SH8, 97WA0). i (969PH0): absolute spectroscopic factors are also given. j (96GR7). k (96GO0). (This footnote is not labeled in the table content.) 4
42 Table.6: 4 N(d, p) N angular distribution studies a E d (MeV) Distribution of proton groups Refs p 0, p, p (97SJ68, 96SJB). p 0, p p 7 (967BE09). p 4 p 7 (969BE08).. p, p, p 4, p, p 6 (969GO4)., 4. p, p (96GO0, 96FI0, 966GA09).. p 0 (96GO, 96FI0, 966GA09).4 p 0, p (969BE08).4. p 0, p p (96KA0) p p, p 7 (96RO) 7, 8, 9 p 8, p 0, p, p 6, p 9, p 0 (969PH0) p 0 (967SC9).8,. p 0 (96MO) 6 p 0 (960MO0) 7 p 0 (96ER0) a See (99AJ76) for earlier references. See also (96JA, 96TE0, 96ST7, 96GOL, 96HEB), (99BOC, 960BEB, 96KOE, 96TAA, 964BAV, 964STJ, 966HOD; theor.), (99AJ76) and 6 O in (97AJ0) N(t, d) N Q m = 4.77 The angular distribution of the deuterons corresponding to the ground state of N has been measured at E t =.0,.8 and.98 MeV. The cross section at E t = MeV is 48 mb: this large value and the energy and angular behavior of the differential cross section suggest that this reaction may proceed by a cluster exchange process (964SC09) N(α, He) N Q m = 9.74 At E α = 6 MeV, the angular distribution of the ground state He particles has been measured by (969GA) and analyzed by DWBA: the ratio of the (α, He) and (α, t) cross sections at this energy is.0 ± 0.. See also (968GAC). 4
43 4. 4 N( 9 Be, 8 Be) N Q m = 9.70 The lifetime of N*(.7) is psec (969NI09): see Table.7 and (967BI). See also (96HOE) N( B, 0 B) N Q m = 0.6 See (967PO). See also (969BRD) N( 4 N, N) N Q m = 0.8 Angular distributions of the transition to the ground state of N have been measured for E( 4 N)(cm) =. to 6 MeV (96TO07, 964JOA, 96BEB, 96HIA). See also (96TO0). Below 6. MeV, the tunneling theory of neutron transfer gives a good account of the data. At higher energies, nuclear absorption of the incident 4 N ions occur (96HIA, 966GA04). See also (968GA0). For reviews of the work on this reaction, see (964FLD, 967DAE, 967VOA, 969BRD). For discussions of relevant theories, see (96BRG, 96BRG, 964BRM, 964GRG, 96BRF, 966BUB, 967BRM, 967BRQ, 967PED, 968MAG, 968NAF, 969KAG) N( 9 F, 8 F) N Q m = 0.40 See (968GA0). 46. C(β ) N Q m = 9.77 The β decay takes place to N*(0,.0, 7.0, 8., 9.0): see Table.. Measurements of γ-ray energies give E γ = 99.0 ± 0.4 kev (967CH9), 8 ± 6 and 9048 ± 4 kev (966AL). See also C. 47. N(γ, n) 4 N Q m = 0.8 See (967ZHA, 968YAE, 969ZHA). 4
44 48. N(γ, p) 4 C Q m = 0.08 The integrated cross section for transitions to 4 C(0) for E γ up to 0. MeV = ± MeV mb, assuming an isotropic angular distribution. Pronounced maxima are observed at E γ = 9., 0.4,.7 and 4. MeV. In addition a pigmy resonance at E γ =. MeV and less pronounced structures at E γ =.6 and 7.0 MeV are also observed (964KO0). See also (96FI04) and (967ZHA, 968YAE, 969UBC, 969ZHA). 49. N(e, e) N Using the harmonic oscillator function, analysis of the scattering of 0 and 400 MeV electrons gives, respectively, r rms =.68±0.0 fm and.6±0.0 fm for N (968DAQ). At E e = 07 MeV, excitation of N*(6.) gives Γ 0 γ (M) =.4 ± 0.7 ev and Γ0 γ (E) = 0.06 ± 0.0 ev: δ(e/m) = 0. ± 0.0 (968BE4). 0. N(n, n) N See 6 N.. 4 N(p, p) N The angular distribution of elastically scattered protons has been measured at E p = 9.8 MeV (969SN04). See also (96NAC).. N( He, He) N At E( He) = 9.8 MeV, a number of inelastically scattered He groups are observed corresponding to states in N: see Table.7. Angular distributions were obtained for a number of these, and were analyzed using a local two-body interaction with an arbitrary spin-isospin exchange mixture (969BA06). See also (968BAE). (969BO) measured the angular distribution of elastically scattered He particles at E( He) = MeV.. N(α, α) N 44
45 Table.7: N levels from N( He, He ) and N(α, α ) N* a (MeV ± kev) L a N* b (MeV) L b ± c c c 9.7 ± ± ± ± 40.4 ± 40.9 ± 40. ± ± 40. ± 40 a ( He, He ): (969BA06). b (α, α ) (966HA9). The E x were determined. c Weakly excited. See also (96BU0, 969BA06). 4
46 The surface thickness a = 0.6 fm, as determined from analysis of the scattering of 44 MeV α-particles from N (968FAA). At E α = 40. MeV, a number of particle groups have been observed, and angular distributions have been measured: see Table.7 (966HA9). See also (96BU0), B(E) /e = 4.9 fm 4 for N*(6.): B(E) /e = 60 fm 6 for both N*(.7, 7.7) (966HA9). See also (969BA06). 4. O(β ) N Q m =.760 See O.. (a) 6 O(γ, p) N Q m =.6 (b) 6 O(e, ep) N Q m =.6 Over the giant resonance region in 6 O, the decay takes place to the odd parity states of N at E x = 0 and 6. MeV as well as to both of the even parity states at E x =.7 and.0 MeV. The branching ratios are functions of the excitation energy in 6 O and of the authors: see (96DE4, 96MA4, 96MO, 966KOG, 966OW0, 967CAC, 967CAP, 968BAL, 969MU07, 969SH0). The results are in fair agreement with the predictions of the single-particle, single-hole theory of photoexcitation of 6 O, although some non-single-particle excitation appears to be necessary in some portions of the 6 O giant resonance: see, e.g. (968BAL). High-energy γ-rays have also reported from the decay of N*(7.0, 8., 9.0, 9.) (968BAL, 969HOT, 969MU07). See also the review in (968SCB), (97JO0, 99BR69, 96SC, 968TU0, 969FR0, 969UL0) and (968ZHB; theor.). The τ m of N*(.7) >> 0. psec; τ m for N*(6., 9.) < 0. psec (969MU07): see also Table.7. For reaction (b), see (96DOA) O(n, d) N Q m = 9.90 Angular distribution of the deuterons corresponding to the ground state of N have been determined at E n = 4.4 MeV (964PA, 96VA0) and at 4 MeV (96GA0). See also (96DIE; theor.) O(p, p) N Q m =.6 At E p = 460 MeV, the summed proton spectrum shows two peaks corresponding to the knowckout of p / and p / protons with binding energies of.4 and 9.0 MeV, respectively [ N*(0, 6.)] (966TY0). See also the discussions in (96CLB, 96RIB), (96FO0, 967FUA), (96BEA, 96BE4; theor.) and (99AJ76). 46
47 8. 6 O(d, He) N Q m = 6.6 Angular distributions of the He groups have been measured at E d = 0 MeV (969PU04: to N*(0,.7,.0)), 8 MeV (968GA: to N(0)), 4.4 MeV (967HI06: to N*(0,.7.0, 6.)), MeV (969KAA, 969KAW: to N(0)), and 8 MeV (969DO04: to N*(0,.7.0, 6.)) and analyzed by DWBA. The He group to N*(.) does not show a stripping pattern (969PU04). See also (968BAJ; theor.) O(t, α) N Q m = Angular distributions have been measured at E t = 0.9 to.7 MeV (967KOG; α 0 ),. to.9 MeV (99JO; α 0 ),. to.0 MeV (966SED; α 0 ), and MeV (96AJ0; α 0, α, α ). A γ-ray with E γ =.7 ± 0.00 MeV has been observed in this reaction: see Table.7 (96AL9). See also (99AJ76) O( 4 N, O) N Q m = 4.8 See (96TOD, 969BRD) O(d, α) N Q m = 9.80 See (94PA9) O(p, α) N Q m =.98 Angular distributions of ground state α-particles are reported at E p = 0.84 to.00 MeV (96CA0) and at 7.9, 0.6 and. MeV (964EC0). Angular correlation measurements lead to J =,, ( ), ( ) for N*(.8, 6., 8., 8.8) (96WA06), J =,,, 7 for N*(.8, 7.6, 7.0, 7.7) (966HA0), J = for N*(6.) (966LO0). The M/E mixing ratio of the 7.0 g.s. transition indicates an unusually large retardation of an E transition in a nonself-conjugate nucleus (966HA0). J = for N*(.7) and the mixing parameter fix J = for N*(0.4) which fed the first excited state of N (99HED) in the 4 C(p, γ) N reaction (96WA06). See also (960CL0, 96LO0, 964AMA, 964MA, 964MA7, 964SC0), (99AJ76) and 9 F in (99AJ76, 97AJ0). 47
48 6. 9 F(γ, α) N Q m = 4.0 See (96HAG). 64. (a) 9 F(p, pα) N Q m = 4.0 (b) 9 F(α, α) N Q m = 4.0 For reaction (a) see (96FO0). For reaction (b) see (96LA0) F(d, 6 Li) N Q m =.9 Angular distributions of the 6 Li ions corresponding to N(0) have been measured at E d = 9.0 to. MeV (967DE4), 4. MeV (964DAB), 4.9 MeV (966DE09) and MeV (96SLC). Attempts have been made to fit the data with DWBA: see references above and (96DRB). See also (964BLC) F( 4 N, 8 F) N Q m = 0.40 See (96WIA). 48
49 O (Figs. and ) GENERAL: Model calculations: (960TAE, 960TAC, 96CO, 96KUB, 964ALL, 964AMD, 964BRH, 964RIA, 96CO, 96GIB, 96GRH, 96GUA, 96HUD, 966BOR, 966EL08, 966RIF, 966SO0, 967BOT, 967EL0, 968DE, 968ELA, 968HOH, 968MAB, 968SH08, 968WOC, 968ZHB, 968ZU0, 969DE6, 969ELB, 969GUM, 969SAJ). General calculations and reviews: (964EVA, 967FAA, 967NED, 968BIC). Electromagnetic transitions: (96RON, 966PO, 966ROP, 966WAE, 967KUE, 967POJ, 967WAC, 968BIC, 968SH08, 968ZHB, 968ZH06, 969KHC, 969ZHA). Other: (966WAK, 967AUB, 969FOD, 969HAG). Ground state: J = (96CO7); µ = nm (96CO7, 964LI4, 967COD). See also (964STB, 96MAT, 966MAV, 967NED, 967SH4, 968PE6, 968ROE, 969FU).. O(β ) N Q m =.760 Reported half-lives are listed in Table.9 (94KL6, 9BA8, 97KI, 97PE, 99KI99, 960JA): the weighted mean is.4 ± 0.6 sec. See also (96CS0, 96VA). Using this value for τ / and Q m, log ft =.64. See also (968BA4) and (96GAD, 966MIF, 967AMH, 968SH08, 969LED, 969SU; theor.).. 7 Li( 4 N, 6 He) O Q m =.687 See (97AL78).. (a) 0 B( 6 Li, n) O Q m =.09 (b) 0 B( 7 Li, n) O Q m = 7.97 See (97NO7). 49
50 Table.8: Energy levels of O a E x (MeV ± kev) J π τ m (psec) or Γ (kev) Decay Reactions 0.8 ±.4 ± ± ± ± ± ± ± ± 6 τ / =.4 ± 0.6 sec β,,, 4, 6, 7, 8, 9, 6, 7, 8, 9, 0,,,, 4,, 6, 7, 8, 9 τ m < 0. psec γ 8, 9, 6, 7,, 4,, 6. ± 0. γ 8, 9, 6, 7, 0,,, 4,, 6 < γ 8, 9, 6, 7,,, 4,, 6 < 0.08 γ 8, 9, 6, 7, ± 0.06 γ 8, 9, 6, 7,, 6 γ 8, 6, 7,, 4, 6 Γ =.7 ± 0. kev γ, p 9, 6, 7,.6 ± 0.7 γ, p 9, 7, γ, p ±.4.7 ± γ, p 8, 9, ±.6 (, ).9 ± 0.4 γ, p 8, 9, 9.48 ± 0. ± 0. γ, p 8, 9, 9.0 ± 40 ( ) 80 ± 4 γ, p ± ± ± 0. γ, p 8, 9,, 4 ± p 8, 0, 9.7 ± 0 (, ) 90 ± 0 γ, p ± 8 6 ± 4 p 0, 0.46 ± 0 47 γ, p 9, 0,, ± 0.99 ± p 0, 84 γ, p 9, 0,.0 ± 7 p 0. ± < 0 p 0.0 ± (, ) 6 γ, p 9, 0,. ± 00 T = 8.6 ± < 0 p γ, p 0.7 ± p 9 0
51 Table.8: Energy levels of O a (continued) E x (MeV ± kev) J π τ m (psec) or Γ (kev) Decay Reactions.6 ± ( ) p 0.7 ± < 0 p 0,.7 ±.846 ± 0.98 ±. ± 80 p 0 0 p 0 0 p 0 60 p 0 ) 60 p 0.47 ± (.8 0 γ, p p p, He, α, 0,. p, d, He, α.4 broad (p, α) 0,.49 ( ) p p, α p γ, p 9 n, p, He, α, 0,, 4.0 ± 40 (, ) 60 ± 0 n, p, He ± p, α 40 ± 0 n, p, He, α, 0,, p, α ± 0 00 ± 0 n, p, He, α, 4.69 ± ± 0 n, p, He, 4.9 ± ± n, p, He,.4 ± 0 6 ± p, He, α.6 ± ± p, He, α.84 ± 0 (, ) 0 n, p, He, α, 6.04 He, α 6.09 n, He, α 6.9 He, α 6.4 ± 0 70 He, α
52 Table.8: Energy levels of O a (continued) E x (MeV ± kev) J π τ m (psec) or Γ (kev) Decay Reactions 6.48 ± 0 60 ± 90 n, p 6.77 ± 0 00 n, He, α 7.0 ± 0 (, ) 600 n, p, He, α 7.99 ± 0 (, ) 00 He, α 8. ± 0 n, p, He 9.0 ± 0 n, He 9.90 ± 0 n, p, He broad γ, p 9 a See also Tables. and.. 4. B( 6 Li, n) O Q m =.7 See (96HOE).. (a) C( He, n) 4 O Q m =.48 E b =.07 (b) C( He, p) 4 N Q m = (c) C( He, d) N Q m =.0 (d) C( He, He) C (e) C( He, α) C Q m =.88 (f) C( He, 8 Be) 7 Be Q m =.78 Excitation functions for these reactions have been measured over a wide range of energies: see Table.0. Observed resonances are displayed in Table.. For discussions of angular distribution measurements which have been measured at many energies over the range displayed in Table.0, see the writeups of 7 Be in (966LA04), C and C in (968AJ0), and N, 4 N, and 4 O. See also (964DEE). Consideration of the relative yields at E( He) =. and. MeV lead to the tentative J π assignments given in Table. for O*(.00,.79) (97BR8). The assignments for O*(4.0, 4.7, 4.46) are derived from analyses of the He elastic scattering, particle and γ 6.44 angular distributions, and the total cross sections of the n 0 and p groups (964KU0). Above E( He) MeV, the excitation functions show broad maxima (see Table.) but it is not
Energy Levels of Light Nuclei A = 20
Revised 20 Manuscript 19 June 2008 Energy Levels of Light Nuclei A = 20 F. Ajzenberg-Selove University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396 Abstract: An evaluation of A = 18 20 was published
LIGHT UNFLAVORED MESONS (S = C = B = 0)
LIGHT UNFLAVORED MESONS (S = C = B = 0) For I = 1 (π, b, ρ, a): ud, (uu dd)/ 2, du; for I = 0 (η, η, h, h, ω, φ, f, f ): c 1 (uu + d d) + c 2 (s s) π ± I G (J P ) = 1 (0 ) Mass m = 139.57018 ± 0.00035
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님 Motivation Bremsstrahlung is a major rocess losing energies while jet articles get through the medium. BUT it should be quite different from low energy
(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)
Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)
Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.
Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +
2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
In your answer, you should make clear how evidence for the size of the nucleus follows from your description
1. Describe briefly one scattering experiment to investigate the size of the nucleus of the atom. Include a description of the properties of the incident radiation which makes it suitable for this experiment.
CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Th, Ra, Rn, Po, Pb, Bi, & Tl K x-rays. Rn Kα1. Rn Kα2. 93( 227 Th)/Rn Kβ3. Ra Kα2. Po Kα2 /Bi K α1 79( 227 Th)/Po Kα1. Ra Kα1 /Bi K β1.
Page -1-10 8 10 7 10 6 10 5 10 4 334 ( Th) Counts/Channel 10 3 10 2 10 1 49 ( Th)/ 50 ( Th)/ 50 ( Fr) 0 100 200 300 400 500 600 700 800 900 1000 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Channel
HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
Engineering Tunable Single and Dual Optical. Emission from Ru(II)-Polypyridyl Complexes. Through Excited State Design
Engineering Tunable Single and Dual Optical Emission from Ru(II)-Polypyridyl Complexes Through Excited State Design Supplementary Information Julia Romanova 1, Yousif Sadik 1, M. R. Ranga Prabhath 1,,
Energy Levels of Light Nuclei A = 14
14 Revised Manuscript 05 November 2012 Energy Levels of Light Nuclei A = 14 F. Ajzenberg-Selove University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396 Abstract: An evaluation of A = 13 15 was
Section 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΤΜΗΜΑ ΦΥΣΙΚΩΝ ΠΟΡΩΝ & ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΤΟΜΕΑΣ ΠΕΡΙΒΑΛΛΟΝΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΕΛΕΓΧΟΥ ΠΟΙΟΤΗΤΑΣ Υ ΑΤΙΚΩΝ & Ε ΑΦΙΚΩΝ ΠΟΡΩΝ ΕΠΙΒΑΡΥΝΣΗ ΜΕ ΒΑΡΕΑ ΜΕΤΑΛΛΑ Ε ΑΦΩΝ ΤΗΣ
Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O
Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.
Nuclear Physics 5. Name: Date: 8 (1)
Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly
DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG
Technical Information T-410A ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 410A Refrigerant (R-410A) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered
Supporting Information
Supporting Information rigin of the Regio- and Stereoselectivity of Allylic Substitution of rganocopper Reagents Naohiko Yoshikai, Song-Lin Zhang, and Eiichi Nakamura* Department of Chemistry, The University
Hadronic Tau Decays at BaBar
Hadronic Tau Decays at BaBar Swagato Banerjee Joint Meeting of Pacific Region Particle Physics Communities (DPF006+JPS006 Honolulu, Hawaii 9 October - 3 November 006 (Page: 1 Hadronic τ decays Only lepton
Energy Levels of Light Nuclei A = 19
9 Revised Manuscript October 08 Energy Levels of Light Nuclei A = 9 D.R. Tilley a,b, H.R. Weller a,c and C.M. Cheves a,c, R.M. Chasteler a,c a Triangle Universities Nuclear Laboratory, Durham, NC 08-008,
EE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Το άτομο του Υδρογόνου
Το άτομο του Υδρογόνου Δυναμικό Coulomb Εξίσωση Schrödinger h e (, r, ) (, r, ) E (, r, ) m ψ θφ r ψ θφ = ψ θφ Συνθήκες ψ(, r θφ, ) = πεπερασμένη ψ( r ) = 0 ψ(, r θφ, ) =ψ(, r θφ+, ) π Επιτρεπτές ενέργειες
4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
CE 530 Molecular Simulation
C 53 olecular Siulation Lecture Histogra Reweighting ethods David. Kofke Departent of Cheical ngineering SUNY uffalo kofke@eng.buffalo.edu Histogra Reweighting ethod to cobine results taken at different
SUPPLEMENTAL INFORMATION. Fully Automated Total Metals and Chromium Speciation Single Platform Introduction System for ICP-MS
Electronic Supplementary Material (ESI) for Journal of Analytical Atomic Spectrometry. This journal is The Royal Society of Chemistry 2018 SUPPLEMENTAL INFORMATION Fully Automated Total Metals and Chromium
1 Decay Scheme. 2 Nuclear Data. 2.1 α Transitions
1 Decay Scheme Cf- disintegrates by alpha emissions mainly to the Cm-248 ground state level, and by spontaneous fission for 3,086(8) %. The average number of neutrons emitted by spontaneous fission is:
Assalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
DuPont Suva 95 Refrigerant
Technical Information T-95 ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered
Dr. D. Dinev, Department of Structural Mechanics, UACEG
Lecture 4 Material behavior: Constitutive equations Field of the game Print version Lecture on Theory of lasticity and Plasticity of Dr. D. Dinev, Department of Structural Mechanics, UACG 4.1 Contents
Homework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
ΓΗ ΚΑΙ ΣΥΜΠΑΝ. Εικόνα 1. Φωτογραφία του γαλαξία μας (από αρχείο της NASA)
ΓΗ ΚΑΙ ΣΥΜΠΑΝ Φύση του σύμπαντος Η γη είναι μία μονάδα μέσα στο ηλιακό μας σύστημα, το οποίο αποτελείται από τον ήλιο, τους πλανήτες μαζί με τους δορυφόρους τους, τους κομήτες, τα αστεροειδή και τους μετεωρίτες.
Example Sheet 3 Solutions
Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note
Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]
d Suva refrigerants Technical Information T-9100SI Thermodynamic Properties of Suva 9100 Refrigerant [R-410A (50/50)] Thermodynamic Properties of Suva 9100 Refrigerant SI Units New tables of the thermodynamic
Math221: HW# 1 solutions
Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin
Derivation of Optical-Bloch Equations
Appendix C Derivation of Optical-Bloch Equations In this appendix the optical-bloch equations that give the populations and coherences for an idealized three-level Λ system, Fig. 3. on page 47, will be
Heterobimetallic Pd-Sn Catalysis: Michael Addition. Reaction with C-, N-, O-, S- Nucleophiles and In-situ. Diagnostics
Supporting Information (SI) Heterobimetallic Pd-Sn Catalysis: Michael Addition Reaction with C-, N-, -, S- Nucleophiles and In-situ Diagnostics Debjit Das, a Sanjay Pratihar a,b and Sujit Roy c * a rganometallics
DuPont Suva 95 Refrigerant
Technical Information T-95 SI DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered
Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil
J. Jpn. Soc. Soil Phys. No. +*0, p.- +*,**1 Eh * ** Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil Daisuke MURAKAMI* and Tatsuaki KASUBUCHI** * The United Graduate
Three coupled amplitudes for the πη, K K and πη channels without data
Three coupled amplitudes for the πη, K K and πη channels without data Robert Kamiński IFJ PAN, Kraków and Łukasz Bibrzycki Pedagogical University, Kraków HaSpect meeting, Kraków, V/VI 216 Present status
; +302 ; +313; +320,.
1.,,*+, - +./ +/2 +, -. ; +, - +* cm : Key words: snow-water content, surface soil, snow type, water permeability, water retention +,**. +,,**/.. +30- +302 ; +302 ; +313; +320,. + *+, *2// + -.*, **. **+.,
C.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Strain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Second Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
Quantitative chemical analyses of rocks with X-ray fluorescence analyzer: major and trace elements in ultrabasic rocks
98 Scientific Note X : Quantitative chemical analyses of rocks with X-ray fluorescence analyzer: major and trace elements in ultrabasic rocks Kimiko Seno and Yoichi Motoyoshi,**- +, +, ;,**. -,/ Abstract:
6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Electronic structure and spectroscopy of HBr and HBr +
Electronic structure and spectroscopy of HBr and HBr + Gabriel J. Vázquez 1 H. P. Liebermann 2 H. Lefebvre Brion 3 1 Universidad Nacional Autónoma de México Cuernavaca México 2 Universität Wuppertal Wuppertal
Areas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Math 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Appendix B Table of Radionuclides Γ Container 1 Posting Level cm per (mci) mci
3 H 12.35 Y β Low 80 1 - - Betas: 19 (100%) 11 C 20.38 M β+, EC Low 400 1 5.97 13.7 13 N 9.97 M β+ Low 1 5.97 13.7 Positrons: 960 (99.7%) Gaas: 511 (199.5%) Positrons: 1,199 (99.8%) Gaas: 511 (199.6%)
derivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.
B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs
CRASH COURSE IN PRECALCULUS
CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter
Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo
Bull. Earthq. Res. Inst. Univ. Tokyo Vol. 2.,**3 pp.,,3,.* * +, -. +, -. Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo Kunihiko Shimazaki *, Tsuyoshi Haraguchi, Takeo Ishibe +, -.
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ
[1] P Q. Fig. 3.1
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
Approximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +
Chapter 3. Fuzzy Arithmetic 3- Fuzzy arithmetic: ~Addition(+) and subtraction (-): Let A = [a and B = [b, b in R If x [a and y [b, b than x+y [a +b +b Symbolically,we write A(+)B = [a (+)[b, b = [a +b
Ψηφιακή ανάπτυξη. Course Unit #1 : Κατανοώντας τις βασικές σύγχρονες ψηφιακές αρχές Thematic Unit #1 : Τεχνολογίες Web και CMS
Ψηφιακή ανάπτυξη Course Unit #1 : Κατανοώντας τις βασικές σύγχρονες ψηφιακές αρχές Thematic Unit #1 : Τεχνολογίες Web και CMS Learning Objective : SEO και Analytics Fabio Calefato Department of Computer
The challenges of non-stable predicates
The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates
Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee
Appendi to On the stability of a compressible aisymmetric rotating flow in a pipe By Z. Rusak & J. H. Lee Journal of Fluid Mechanics, vol. 5 4, pp. 5 4 This material has not been copy-edited or typeset
Αλληλεπίδραση ακτίνων-χ με την ύλη
Άσκηση 8 Αλληλεπίδραση ακτίνων-χ με την ύλη Δ. Φ. Αναγνωστόπουλος Τμήμα Μηχανικών Επιστήμης Υλικών Πανεπιστήμιο Ιωαννίνων Ιωάννινα 2013 Άσκηση 8 ii Αλληλεπίδραση ακτίνων-χ με την ύλη Πίνακας περιεχομένων
MSM Men who have Sex with Men HIV -
,**, The Japanese Society for AIDS Research The Journal of AIDS Research HIV,0 + + + + +,,, +, : HIV : +322,*** HIV,0,, :., n,0,,. + 2 2, CD. +3-ml n,, AIDS 3 ARC 3 +* 1. A, MSM Men who have Sex with Men
Other Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Calculating the propagation delay of coaxial cable
Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric
Srednicki Chapter 55
Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή
Areas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
An experimental and theoretical study of the gas phase kinetics of atomic chlorine reactions with CH 3 NH 2, (CH 3 ) 2 NH, and (CH 3 ) 3 N
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2015 An experimental and theoretical study of the gas phase kinetics of atomic chlorine
Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Electronic Supplementary Information:
Electronic Supplementary Information: 2 6 5 7 2 N S 3 9 6 7 5 2 S N 3 9 Scheme S. Atom numbering for thione and thiol tautomers of thioacetamide 3 0.6 0. absorbance 0.2 0.0 0.5 0.0 0.05 0.00 N 2 Ar km/mol
Η ΕΠΙΔΡΑΣΗ ΤΗΣ ΑΙΘΑΝΟΛΗΣ,ΤΗΣ ΜΕΘΑΝΟΛΗΣ ΚΑΙ ΤΟΥ ΑΙΘΥΛΟΤΡΙΤΟΤΑΓΗ ΒΟΥΤΥΛΑΙΘΕΡΑ ΣΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΗΣ ΒΕΝΖΙΝΗΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΑΒΑΛΑΣ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΚΩΝ ΕΦΑΡΜΟΓΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η ΕΠΙΔΡΑΣΗ ΤΗΣ ΑΙΘΑΝΟΛΗΣ,ΤΗΣ ΜΕΘΑΝΟΛΗΣ ΚΑΙ ΤΟΥ ΑΙΘΥΛΟΤΡΙΤΟΤΑΓΗ ΒΟΥΤΥΛΑΙΘΕΡΑ ΣΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΗΣ ΒΕΝΖΙΝΗΣ ΟΝΟΜΑΤΕΠΩΝΥΜΟ
Νόµοςπεριοδικότητας του Moseley:Η χηµική συµπεριφορά (οι ιδιότητες) των στοιχείων είναι περιοδική συνάρτηση του ατοµικού τους αριθµού.
Νόµοςπεριοδικότητας του Moseley:Η χηµική συµπεριφορά (οι ιδιότητες) των στοιχείων είναι περιοδική συνάρτηση του ατοµικού τους αριθµού. Περιοδικός πίνακας: α. Είναι µια ταξινόµηση των στοιχείων κατά αύξοντα
ST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Σπανό Ιωάννη Α.Μ. 148
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΙΣ ΠΕΡΙΒΑΛΛΟΝΤΙΚΕΣ ΕΠΙΣΤΗΜΕΣ Ηλεκτροχημική εναπόθεση και μελέτη των ιδιοτήτων, λεπτών υμενίων μεταβατικών μετάλλων, για παραγωγή H2 Διπλωματική
Υπολογιστική Φυσική Στοιχειωδών Σωματιδίων
Υπολογιστική Φυσική Στοιχειωδών Σωματιδίων Όρια Πιστότητας (Confidence Limits) 2/4/2014 Υπολογ.Φυσική ΣΣ 1 Τα όρια πιστότητας -Confidence Limits (CL) Tα όρια πιστότητας μιας μέτρησης Μπορεί να αναφέρονται
Section 7.6 Double and Half Angle Formulas
09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)
ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:
4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES. Reading: QM course packet Ch 5 up to 5.6
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES Readig: QM course packet Ch 5 up to 5. 1 ϕ (x) = E = π m( a) =1,,3,4,5 for xa (x) = πx si L L * = πx L si L.5 ϕ' -.5 z 1 (x) = L si
Tridiagonal matrices. Gérard MEURANT. October, 2008
Tridiagonal matrices Gérard MEURANT October, 2008 1 Similarity 2 Cholesy factorizations 3 Eigenvalues 4 Inverse Similarity Let α 1 ω 1 β 1 α 2 ω 2 T =......... β 2 α 1 ω 1 β 1 α and β i ω i, i = 1,...,
SMD Transient Voltage Suppressors
SMD Transient Suppressors Feature Full range from 0 to 22 series. form 4 to 60V RMS ; 5.5 to 85Vdc High surge current ability Bidirectional clamping, high energy Fast response time
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Το franchising ( δικαιόχρηση ) ως µέθοδος ανάπτυξης των επιχειρήσεων λιανικού εµπορίου
UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:
UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,
Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1
Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the
AME SAMPLE REPORT James R. Cole, Ph.D. Neuropsychology
Setting the Standard since 1977 Quality and Timely Reports Med-Legal Evaluations Newton s Pyramid of Success AME SAMPLE REPORT Locations: Oakland & Sacramento SCHEDULING DEPARTMENT Ph: 510-208-4700 Fax:
Matrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Monolithic Crystal Filters (M.C.F.)
Monolithic Crystal Filters (M.C.F.) MCF (MONOLITHIC CRYSTAL FILTER) features high quality quartz resonators such as sharp cutoff characteristics, low loss, good inter-modulation and high stability over
Si + Al Mg Fe + Mn +Ni Ca rim Ca p.f.u
.6.5. y = -.4x +.8 R =.9574 y = - x +.14 R =.9788 y = -.4 x +.7 R =.9896 Si + Al Fe + Mn +Ni y =.55 x.36 R =.9988.149.148.147.146.145..88 core rim.144 4 =.6 ±.6 4 =.6 ±.18.84.88 p.f.u..86.76 y = -3.9 x
1 Decay Scheme. 2 Nuclear Data. 2.1 Electron Capture Transitions. 2.2 β Transitions
1 Decay Scheme Le césium se désintègre essentiellement par émission bêta moins vers des niveaux excités du baryum. Cs- desintegrates mainly by beta minus emissions to excited levels in Ba-. 2 Nuclear Data
Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz
Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)
12 2006 Journal of the Institute of Science and Engineering. Chuo University
12 2006 Journal of the Institute of Science and Engineering. Chuo University abstract In order to study the mitigation effect on urban heated environment of urban park, the microclimate observations have
ΠΕΡΙΟΔΙΚΟΣ ΠΙΝΑΚΑΣ ΣΤΟΙΧΕΙΩΝ
ΠΕΡΙΟΔΙΚΟΣ ΠΙΝΑΚΑΣ ΣΤΟΙΧΕΙΩΝ Περίοδοι περιοδικού πίνακα Ο περιοδικός πίνακας αποτελείται από 7 περιόδους. Ο αριθμός των στοιχείων που περιλαμβάνει κάθε περίοδος δεν είναι σταθερός, δηλ. η περιοδικότητα
ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ
ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ Τομέας Περιβαλλοντικής Υδραυλικής και Γεωπεριβαλλοντικής Μηχανικής (III) Εργαστήριο Γεωπεριβαλλοντικής Μηχανικής TECHNICAL UNIVERSITY OF CRETE SCHOOL of
Statistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?
Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least