Shell model approach to N Z medium-heavy nuclei using extended P+QQ interaction
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1 Shell model approach to N Z medium-heavy nuclei using extended PQQ interaction M. Hasegawa Topics: Structure of N Z medium-heavy nuclei, Large-scale shell model calculations, Extended PQQ interaction (EPQQ). based on the collaboration with K. Kaneko and T. Mizusaki
2 1. At the end of the th century --- Shell model study of -shell nuclei --- f 7 / SM had succeeded for sd shell nuclei using realistic effective interaction USD B.A. Brown & B.H. Wildenthal, Ann. Rev. Nucl. Part. Sci., 8(1988), 9 realistic effective interaction for pf shell KB A. Poves & A.P. Zuker, Phys. Rep., 7(1981), FPD W.A. Richter, B.A. Brown, Nucl. Phys. (1991), Caurier s calculation code full pf shell model calculations for A = 8, odd nuclei A = 7,9, E. Caurier, A.P. Zuker, A. Poves, G. M., Phys. Rev. C, (199),
3 G. Martinez-Pinedo, A. Zuker, A. Poves, E. Caurier, Phys. Rev. C (1997), 187.
4 Better effective interaction was required. for heavier pf shell nuclei KBG, applied to A =,1,
5 A. Poves, et al.,nucl-th/177.
6 Monte Carlo shell model a. S.E. Koonin, D.J.Dean, and K. Langange, Phys. Rep., 78(1997),. b. M. Honma, T. Mizusaki, and T. Otsuka, Phys. Rev. Lett., 77(199), 1. Shape coexistence in Ni. T. Mizusaki, T. Otsuka, Y. Utsuno, M. Honma, T. Sebe, P. R. C., 9(1999), R18. >
7 T. Mizusaki, T. Otsuka, Y. Utsuno, M. Honma, T. Sebe, P. R. C., 9(1999), R18.
8 . Various collective models and our approach Collective models RPA IBM Mean field approximations HF, HFRPA HFB using PQQ force, Skyrme force, etc. VAMPIR A. Petrovici, et al., Nucl. Phys. A8(1988), 17. Projected SM Y. Sun, nucl-th/11. K. Hara & S. Iwasaki, Nucl. Phys. A(1979), 1.
9 M. Yamagami, K. Matsuyanagi, M. Matsuo, Nucl. Phys. A9(1), 79
10 A. Petrovici, K.W. Scmid, A. Faessler, Nucl. Phys. A71(),.
11 Y. Sun, nucl-th/11.
12 We investigated T= and T=1 pairing correlations by means of the shell model with PQQ. Important T= monopole field V T = πν = k a b JM A JMT = ( ab) AJMT = ( ab) can explain the binding energy. M. Hasegawa & K. Kaneko, Phys. Rev. C, 9(1999), 19. adding quadrupole pairing force, etc., and T= and T=1 monopole corrections, Extended PQQ int. is more than a toy interaction. f 7 / successfully describes -shell nuclei. M. Hasegawa & K. Kaneko, N. P. A, 7(), 11; 88(1), 7.
13 Energy (MeV) 8 T= T=1 T=1 T= , V T = πν 1 = k n v n ( v { 1) T ) } τ= πν QQ P P V SLG 1 9 P P QQ τ= πν V SLG ( ) g g 9/ n p n n systems n p =n n =1 n p =n n =
14 Excitation energy (MeV) T=1 T= T= T= ( ) g g 9/ systems n p n n EPQQ FEI SLG EPQQ FEI SLG n p =n n = n p =n n =
15 Energy (MeV) 1 B.E. n p =n n =n/ SLG (T=) SLG (T=1) k = k =.9 ( g9/ g ) n systems n
16 V T=1 T=, Excitation energy (MeV) (,) (7) () (1,) 1() is adjusted. 1 EPQQ FEI Expt KB FPD
17 18 A= 8 / / Mn / Excitation energy (MeV) Cr,J=even Cr,J=odd Mn,T= Expt. Calc. Excitation energy (MeV) / 1/ 19/ 17/ 1/ 1/ 9/ 11/ 1/ 1/ 1/ 9/,11/ / 7/ / / 1/ 19/ 17/ 1/ 1/ 9/ 11/ 1/ / 1/ 1/ 9/,11/ 7/ / / 1/ 19/ 17/ 1/ 1/ 1/ 9/ 11/ / 1/ 1/ 9/ 11/ 7/ / 1 1 J / 7/ / 7/ / 7/ D E exp
18 . About effective interaction Realistic effective interactions ~ EPQQ H H sp V T = πν ΔV pointed out by A.P. Zuker, M. Dufour,.. P. R. C., (199), 11. mc V ( P ) V ( P ) V ( QQ) V ( OO)... J. Duflo,.. P. R. C., 9(1999), R7. Our calculations proved this concretely. Shell model with EPQQ
19 V m (j a,j b ) (MeV) :d/, :d/ :p1/ 1 7 a,b 1,1 1, 1, USD, (a),, T=1 T= V = πν k A T = a b JM ( ab) AJMT ( ab) JMT = = V m (j a,j b ) (MeV) a,b (b) 1:f7/, :p/, :f/, :p1/ 1,1 1, 1, 1,,,,, KB(T=) KB(T=1) fpd(t=) fpd(t=1) EPQ(T=) EPQ(T=1),, T=1 T= K. Kaneko, M. Hasegawa, Prog. Theor. Phys. 1(1),1179.
20 Better effective interactions are desired. GXPF1 by M. Honma et al., Phys. Rev. C, (), 11 There are many interesting phenomena in pf-shell nuclei, which could be investigated by using GXPF1 int. Study heavier nuclei as well as light ones!
21 . Our work Large-scale shell model calculations with EPQQ Mizusaki s calculation code T. Mizusaki, RIKEN Accel. Prog. Rep., (), 1. N A= 1 Physics: Z nuclei with When Z, N, and J increase, structure changes rapidly, change in shape, shape coexistence, particle alignments, Ge: quadrupole and octupole corr.
22 Observed heaviest N=Z nucleus 88 Ru ( p 1 /, f/, p1/, g9/ ) full SM cal. with maximum dimension explains difference of backbending between 88 Ru and 9 Ru, and gives good prediction for 89 Ru. Advantages: describes odd and even-even nuclei using the same parameters, better than the mean field approx, etc.
23 back to Ge isotopes
24 8Ge D. Ward, Phys. Rev. C (1), 11.
25
26
27
28 Ge E.A. Stefanova, Phys. Rev. C 7(), 19.
29 back to Ge isotopes Parameter search using EPQQ including s. p. energies. reproduces well a lot of energy levels, different bands, B(E) values of collective bands, Q moments. Advantages: strict wave functions cal. of j a,,,, a t n n π a ν a T= proton-neutron alignment in even-even, odd, and odd-odd nuclei, successive alignments with increasing J. M. H., K. Kaneko, and T. Mizusaki, P. R. C, 7(), 11(R), 71(), 1.
30 Excitation energy (MeV) (7) (1) 19 (17) (1) (11) 7 17 (1) (11) π= π= exp cal exp cal Ge () (1) (19) (1) 1, (17) Ge
31 (a) Ge π = 18 Spin J ( h ) 1 1 nd band exp cal J=odd exp cal J=even exp cal (b) Ge π = yrast Spin J ( h ) J=odd exp cal J=even 7 exp cal. 1 (E J E J )/ (MeV)
32 exp cal 8 Ge π= π= π= π= Excitation energy (MeV) 18, ,
33 <n(g )> 9/ 1 8 Ge g9/ g9/ T J neutron proton J J
34 8 Ge evenj, π = Excitation energy (MeV) 1 1 cal 1p1nal 1p1n-al band 8 18 pnal pn-al band band on 18 nal n-al band band on 1 exp band on 8 gs band 1 gs band J
35 T pf y = or T pf T g 9/ T pf Tg 9/ T pf y = J pf or J pf J g 9/ y=j J pf J pf 8 J g 8 9/ 18 Jg 9/ 18 Jg 9/ 8 Ge J
36 Shape transition in Zn, Ge, 8 Se, ( 7 Kr) prolate, oblate(coexisting prolate) triaxial K. Kaneko et al, Phys. Rev. C, 7()., 11. using the successful Hamiltonian, constrained HF calculation. T. Mizusaki et al., P. R. C, 9(1999). 18(R). Isomeric states in odd-odd As, and 7 As Phys. Lett. B, 17(), 1. detailed structure of odd nucleus 9 As Phys. Rev. C, 7(),.
37 [ γ =] Spectroscopic Q moment (e fm ) 1 1 cal cal 1 Ge Ge Zn Zn 7 Ge 1 exp Q( ) 8 Zn, Zn exp Q( 1 ) (a) Ge [ γ =] q (fm ) (b) 8 Ge minimum q (fm ) N= N= N= N=8 (c) 7 Ge q (fm )
38 Y SHFWURVFRSLFTXDGUXSROHPRPHQWHIP Y =Q *H H K. Kaneko, M. Hasegawa, T. Mizusaki, Phys. Rev. C., 7(), 11.
39 1 As Excitation energy (MeV) 1 8 * (18) (1) (1) (1) T=1 T= T=1 T= exp cal
40 I. Stefanescu et al., Phys. Rev. C., 79(). 9As
41 9As Excitation energy (MeV) ( ) (9 ) ( ) ( ) exp pn 9, 1, 7 1pn 1 7 (g9/ 9 ) cal
42 9As Excitation energy (MeV) Bands 7 8 ( ) (9 ) (1 ) (7 ) ( ) ( ) ( ) (1 ) exp Bands cal
43 . Problems Present EPQQ fits for a narrow region A= 7. desired a better fit for N=Z nuclei, Lowering of g9/ near N, Z =? Drastic change at N = in Ge isotopes. Drastic change from 8 Se to 7 Kr. N > Z nuclei, many interesting phenomena, open for shell model.
44 E. Padilla-Rodal et al., P. R. L., 9(), 191.
45 M.Marginean et al., P. R. C., (1), 1.
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