Particle excitations and rotational modes in nuclei with A 70-90

Transcription

1 / , 4. 1 I J E J K J B H A H H A F D O I E Particle excitations and rotational modes in nuclei with A 7-9 In nuclei of the mass region with A 7-9 both protons and neutrons fill the fp shell and the high-j g 9/2 orbitals. In this mass region, small variations of the particle numbers cause drastic changes of the properties of the nuclei. We may study diverse phenomena of the nuclear manybody system such as: Collective rotation in well deformed nuclei Band termination Magnetic rotation in weakly deformed nuclei Particle excitations in nearly spherical nuclei

2 The two ways that a nucleus can generate angular momentum J J j j j j ( 23/2 ) () 31/2 () 29/2 () 27/ () 25/ (25/2 ) (23/2 ) (25/2 ) ( 23/2 ) Y / / / /2 ( 15/2 ) (19/2 ) _ (19/2 ) _ 21/2 _ 19/2 _ 17/2 _ 15/ /2 11/2 7/ /2 _ / / /2 3/ / _ 1/2 collective (classical) in deformed nuclei noncollective (quantal) in nearly spherical nuclei

3 Nuclear chart around A 7-9 Z Se N = Z N = 5 76Sr 77Sr 78Sr 79Sr 8Sr 81Sr 82Sr 83Sr 84Sr 85Sr 86Sr 87Sr 88Sr 74Rb 75Rb 76Rb 77Rb 78Rb 79Rb 8Rb 81Rb 82Rb 83Rb 84Rb 85Rb 86Rb 87Rb 72Kr 73Kr 74Kr 75Kr 76Kr 77Kr 78Kr 79Kr 8Kr 81Kr 82Kr 83Kr 84Kr 85Kr 86Kr 7Br 71Br 72Br 73Br 74Br 75Br 76Br 77Br 78Br 79Br 8Br 81Br 82Br 83Br 84Br 85Br 69Se 7Se 71Se 72Se 73Se 74Se 75Se 76Se 77Se 78Se 79Se 8Se 81Se 82Se 83Se 84Se N β

4 Proton-rich nuclei around A = 7 The nuclei are close to N = Z. Protons and neutrons occupy nearly identical orbits. Competing deformed shell gaps may cause coexisting nuclear shapes and shape changes. Open problems in the understanding of the nuclear manybody system: - How do the individual orbits affect the nuclear shape? - Are there experimental fingerprints of triaxial deformation?

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7 EUROBALL III experiment Detectors: 15 CLUSTER and 26 CLOVER detectors (total of 29 detectors) ISIS Si ball (4 E - E telescopes) Neutron wall (5 liquid scintillation detectors) Reaction: 4 Ca 4 Ca; E = 185 MeV; σ T 16 mb Reaction channels: 4 Ca( 4 Ca,1α3p1n) 72 Br ( 4 % σ T ) 4 Ca( 4 Ca,1α3p) 73 Br ( 4 % σ T ) Target:.9 mg/cm 2 self-supporting (enrichment %) Total number of recorded events: of fold three or higher

8 EUROBALL III experiment Channel selection: 4 Counts* γγ Se 2α2p 72 Se 1α4p 121 Counts* p γγ Br 1α3p 75 Kr 4p1n 72 Se 1α4p 75 Br 76 Kr 5p 4p Counts* n γγ Kr 4p1n Counts* α1n γγ Br 124 1α3p1n Energy (kev)

9 A st Gate Counts / B 1471 C Energy (kev) st Gate

10 Experimental results Preliminary level scheme of 73 Br deduced from the present work.

11 Cranked Nilsson-Strutinsky calculations for 73 Br by I. Ragnarsson and A. Afanasjev (Details of the model: Nucl. Phys. A 68 (1996) 176) Possible configurations include excitations in the orbitals: f 5/2, p 3/2, p 1/2 and g 9/2 Protons (f 5/2 p 3/2 ) 4 (g 9/2 ) 3 J max = 33/2 (f 5/2 p 3/2 ) 5 (g 9/2 ) 2 J max = 27/2, 29/2 Neutrons (f 5/2 p 3/2 ) 6 (g 9/2 ) 4 J max = 18 (f 5/2 p 3/2 ) 7 (g 9/2 ) 3 J max = 15, 16 Possible configurations of the bands: Notation ( π(f 5/2 p 3/2 ) p π(g 9/2 ) p ν(f 5/2 p 3/2 ) n ν(g 9/2 ) n) Band A: (43 64) J π max = 69/2 Band B: (43 73) J π max = 63/2 Band C: (52 64) J π max = 63/2

12 Cranked Nilsson-Strutinsky calculations for 73 Br by I. Ragnarsson and A. Afanasjev (Details of the model: Nucl. Phys. A 68 (1996) 176) 4. [43,7 3 ] E.2535 I(I1) (MeV) Theory [5 2,64] [5 2,64] 1. [43,64] E.2535 I(I1) (MeV) Experiment Band A (,1/2) Band B (, 1/2) Band C (,1/2) Spin (hbar)

13 Cranked Nilsson-Strutinsky calculations for 73 Br by I. Ragnarsson and A. Afanasjev (Details of the model: Nucl. Phys. A 68 (1996) 176) ε 2 sin ( γ 3 ) [43,7 3 ], [5 2,64], [5 2,64], [43,64], ε 2 cos ( γ 3 )

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15 Nuclear rotation: E = h2 2Θ J(J 1); E γ J electric rotation magnetic rotation J x z B(E2) Q 2 B(M1) µ 2 4 E γ ~ const. counts E γ E2 E2 M1 M1 M1 M1 E2 E2 E2 M1 M1 M1 E2 E2 M1 M1 M1 E2 E2 M1 M1 M1 E2

16 Appearance of magnetic rotation Small deformation small E2 transition strengths Protons are particle-like and neutrons are hole-like Protons occupy orbits with small K Neutrons occupy orbits with large K (or vice versa) The rotational axis is tilted relative to the principal axes A large transverse magnetic moment is generated large M1 transition strengths Regular bands are formed Particle spins align to generate high total spin B(M1) decrease with increasing spin

17 Multidetector array GASP (INFN - LN Legnaro)

18 Experiment at XTU tandem in Legnaro Reaction 11 B 76 E = 5 MeV Reaction channels: 76 Ge( 11 B,4n ) 83 Rb ( 5% σ f ) 76 Ge( 11 B,3n ) 84 Rb ( 1% σ f ) 76 Ge( 11 B,5n ) 82 Rb ( 2% σ f ) Target: 76 Ge,.4 mg cm 2 Spectrometer: GASP Recorded events: of fold three or higher

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22 Possible qp excitations in 82,84 Rb and 83 Rb two unpaired nucleons in 82 Rb and 84 Rb: πg 9/2 and νg 9/2 breaking up an πfp pair and lifting one proton to the g 9/2 orbital: lowest-lying 4-qp configuration: π(fp) πg 2 9/2 νg 9/2 one unpaired nucleon in 83 Rb: πg 9/2 breakup of a neutron pair necessary: possible 3-qp configuration: πg 9/2 ν(fp) νg 9/2 may drive the nucleus to nearly spherical shapes where the shears mechanism cannot sustain.

23 Tilted-axis-cranking-model calculations π = M1 band in 82 Rb; configuration π(fp) πg 2 9/2 νg 9/ Rb ε 2 =.16 γ = 2 o J TAC 12 1 EXP B(M1)/B(E2) ((µ N /eb) 2 ) γ= o γ=2 o γ=1 o TAC EXP h _ ω (MeV)

24 Tilted-axis-cranking-model calculations π = M1 band in 84 Rb; configuration π(fp) πg 2 9/2 νg 9/ Rb ε 2 =.14 γ = 15 o J TAC EXP B(M1)/B(E2) ((µ N /eb) 2 ) TAC γ= 15 o γ= 1 o EXP γ= o h _ ω (MeV)

25 Experimental results π = M1 band (C) in 83 Rb Rb J EXP band C B(M1)/B(E2) ((µ N /eb) 2 ) 2 EXP band C h _ ω (MeV)

26 Experimental results Preliminary level scheme of 79 Br deduced from the present work.

27 Tilted-axis-cranking-model calculations π = M1 band in 79 Br; configuration πg 9/2 νg 9/2 ν(fp) ε 2 =.2 γ = TAC J 12 1 EXP h _ ω (MeV)

28 Tilted-axis-cranking-model calculations π = M1 band in 79 Br; configuration πg 9/2 νg 9/2 ν(fp) B(M1) (µ 2 N ) TAC ε 2 =.2 γ = γ = 2 o γ = 2 o EXP B(E2, J=2) (e 2 b 2 ).1.5 TAC EXP. B(M1)/B(E2) (µ 2 N /e2 b 2 ) 4 2 EXP TAC h _ ω (MeV)

29 Conclusions The regular magnetic dipole bands in 82 Rb and 84 Rb are the first evidence of magnetic rotation in the mass region with A 8 (H.Schnare et al., PRL 82 (1999) 448). They can be described in the tilted-axis cranking model on the basis of the 4-qp configuration π(fp) πg 2 9/2 νg 9/2. Magnetic dipole sequences in the odd-even nucleus 83 Rb are not regular. The break-up of a neutron pair may drive the nucleus to deformations (ɛ 2, γ) where shears configurations do not occur. The magnetic dipole band in 79 Br represents a transitional case with a strong magnetic component, but also contributuions from collective rotation.

30 (15/2 ) _ 21/ /2 ( _ ) (11/2 ) _ 19/2 17/2 13/2 τ = 1.4 µs 9/2 _ 5/ /2 (19/2 ) _ 21/2 ( ) ( _ 19/2 ) ) ) _ ) ) ( ) ) ( 15/2 17/2 _ ( ) 11/2 13/2 15/2 ) _ ( _ ( _ _ 15/2 ( () 11/ (11/2 (11/2 ) 13/ /2 ( _ ) 7/2 _ ( 17/2 _ Rb 48 (17/2 ) /2 23/ / /2 29/2 25/2 27/

31 Shell-Model calculations Configuration space: π (Code: RITSSCHIL) ν 1d 5/2 g 1p 1p 9/2 1/2 3/2 g 1p 9/2 1/2 5 f 5/2 Core Ni38 28 Two-body matrix elements: ππ empirical from fit to N=5 nuclei, 78 Ni core; X. Ji and B.H. Wildenthal 1988 πν, νν empirical from fit to N =48,49,5 nuclei (g 9/2,1p 1/2 ) 88 Sr core; R. Gross and A. Frenkel 1976 πν experimental from transfer reactions; (πf 5/2,νg 9/2 ) P.C. Li et al νν experimental from energies of the (g 9/2,1d 5/2 ) ν(g 9/2,1d 5/2 ) multiplet in 88 Sr; P.C. Li and W.W. Daehnick 1987 remaining MSDI; K. Muto et al. 1984

32 Shell-model calculations for 83 Br 48 and 85 Rb 48 Configuration space: π(f 5/2, 1p 3/2, 1p 1/2, g 9/2 ) ν(g 9/2, 1p 1/2 ) 83 Br Rb 48 (MeV) (E - E ) 9/ /2 17/2 13/2 9/2 12 EXP 7 _4 3 _ B(E2) Q (W.u.) (efm ) -74 _ SM /2 17/2 13/2 9/ EXP B(E2) Q (W.u.) (efm ) _1 _ 3 _ SM Regular level spacings up to J = 17/2 and slightly collective B(E2) values result from a coherent superposition of many contributing components including π(fp) and ν(g9/2 2 ) excitations.

33 Shell-model calculations for 85 Rb 48 Configuration space: π(f 5/2, 1p 3/2, 1p 1/2, g 9/2 ) ν(g 9/2, 1p 1/2 ) (MeV) E Rb 33/2 31/2 29/2 27/2 25/2 23/2 21/ ( 11 5 ) ( ).9( ) <.4.4( 2) ( ) 3 B(M1) (W.u.) π ( f 5/ p 3/2 g 9/2 33/2 31/2 29/2 27/2 25/2 23/2 21/2 ) ν ( g -2 9/2 ) 8 3 EXP SM 1 π ( g 9/2 ) ν ( g 9/2-2 ) 8 J J ν = 8 ν = 8 9/2 9/2 9/2 J π Recoupling J π Recoupling J ν = 8 J π Large B(M1) values occur between states that arise from one configuration by recoupling the spin vectors of the involved proton and neutron orbitals.

34 Comparison of shell-model states in 85 Rb and 87 Y (E E 9/2 ) (MeV) positive parity shell model states B(σλ) (W.u.) 2 x x Rb 87 Y (E E 21/2 ) (MeV) negative parity shell model states B(σλ) (W.u.) x x 1 7 M1 E2 85 Rb 87 Y To generate negative-parity states with J 25/2 in 85 Rb requires to excite two protons from the (f 5/2, 1p 3/2 ) subshell into the g 9/2 orbital. In negative-parity states up to J = 33/2 in 87 Y only one proton is lifted over the shell gap at Z = 38 into the g 9/2 orbital.

35 Conclusions In nuclei with N = 48 an onset of collectivity can be observed: The yrast sequences have regular level spacings up to J π = 17/2. The E2 transition strengths have slightly collective values of B(E2) 15 W.u. The shell-model calculations reproduce these properties as a result of the coherent superposition of many contributing components including π(fp) and νg9/2 2 excitations. This interpretation shows that the shell model can describe collective phenomena to a certain extent. The high-spin states form multiplet-like J = 1 sequences with large M1 transition strengths of B(M1) 2 µ 2 N. The shell-model calculations describe these states as recoupled members of seniority υ = 3 and υ = 5 multiplets. The large M1 transition strengths arise from the recoupling of the spins of the involved proton and neutron orbitals. This recoupling of the spin vectors is an analogue to the shears mechanism described in the TAC model.