Systematic features in the low-frequency excitation spectra of even-even nuclei near the closed shell

Volume 46B, number 2

PHYSICS LETTERS

SYSTEMATIC FEATURES

17 September 1973

IN THE LOW-FREQUENCY

EXCITATION

SPECTRA OF EVEN-EVEN NUCLEI NEAR THE CLOSED SHELL M. SAKAI Institute for Nuclear Study, Umverstty of Tokyo, Japan Received 20 July 1973 The trends and regularities in the low-frequency excitation spectra of even-even nuclei were investigated. They may provide a strong challenge to a better understanding of these spectra and the low-frequency nuclear excitation. first 2 + level at an excitation energy nearly equal each other. Especially, there is a wide overlap in Te and Cd isotopes. The energies are almost equal within 50 keV. It may imply that the proton particle orbitals outside of the 50 proton closed shell and the proton hole orbltals inside of the 50 proton closed shell have about the same role for the low-frequency nuclear excitation. The similar features were also observed for the first 4 +, excited 0 +, second 2 + and first 3 + levels. This regularity may show a possibility that the two nuclear regions can be understood in a unified way. A simple theoreti. cal consideration shows that it results from the special situation for these nuclear regions where the parucle and hole orbitals involved in the nuclear excitation

Particle and hole symmetry in nuclear collective excitation o f evene-even nuclei with Z ~ 50. Presence of two new quasi-deformed regions has been well known. One is the neutron deficient region ofTe, Xe, Ba and Ce isotopes and the other is the neutron rich region of Cd, Pd, Ru, Mo and Zr isotopes. These two regions have been discussed so far independently. However, if the energies of the low-lying collective levels are presented as a function of neutron number, we can notice clearly that there exists an intimate relationship between these two nuclear regions. Fig. 1 shows the energy systematics of the first 2 + states. We can notice clearly that the isotone pairs, Cd and Te, Pd and Xe, Ru and Ba and Mo and Ce, that is, the isotopes with Z = 50 +-z have the

>

1.0

1 0,1

LU 0.5

Q 1 54

1 56

I 58

I

1

I

I

60

62

64

66 -

I

I

I

I

I

I

68

70

72

74

76

78

N

Fig. 1. Energy systematics of the first 2+ states as a function of neutron number. The center is taken to be the middle of the neutron major shell from 50 to 82. The expertmental data are taken from ref. [6]. 167

Volume 46B, number 2

PHYSICS LETTERS

17 September 1973

Table 1 Systematic features in the energy ratios of the first 4 + and 2+ levels m closed shell -+2 nucleL 28 neutron closed shell N

26

28

30

Z

E2

R4

E2

R4

E2

R4

R 4 (26)/R4(30)

22(Ti)

0.983

2.334

1.555

1.723

1 05

2 16

1.11

24(Cr)

0.783

2 400

1 434

1.652

0 835

2.19

1.10

26(Fe)

0.84

2.82

1 408

1 804

0.847

2 424

1 16

28 proton closed shell Z

26(Fe)

28(Ni)

30(Zn)

N.

E2

R4

E2

R4

E2

R4

R 4 (26)/R4(30)

30

0.847

2.424

1 454

1.691

1 019

2.17

1 12

32

0.811

2.562

1 323

1.881

0 954

2.200

1.15

34

0 823

2.569

1.173

1.992

0.992

2.340

1.09

50 neutron closed shell N

48

50

52

Z

E2

R4

E2

R4

E2

R4

R4(48)/R4(52)

36(Kr)

0.882

2.376

1 565

1.44

0.775

2.035

1.18

40(Zr)

1.058

2.02

2.182

1.41

0.935

1.600

1.27

42(Mo)

0.948

2.11

1.511

1.51

0.870

1.807

1.17

50 proton closed shell Z

48(Cd)

50(Sn)

52(Ye)

N

E2

R4

E2

R4

E2

R4

R4(48)/R4(52)

62

0.658

2.345

1.260

1.788

0.709

2.093

1.13

64

0.617

2.291

1.300

1.683

0.679

2.003

1.14

66

0.558

2.301

1.293

1.84

0.606

1.992

1 15

68

0.514

2.374

1.229

1.855

0.560

2.072

1.14

70

0.488

2 388

1.172

1.874

0.564

2.09

1.13

72

0.506

2.379

1.140

1.883

0 602

2.072

1.15

74

0 570

2.333

1.139

1.85

0.666

2.04

1.15

82 neutron closed shell N

80

82

84

Z

E2

Ra

E2

R4

E2

R4

R4(80)/R4(82)

54(Xe)

0.847

2.044

1.313

1.291

0 590

1.818

1.12

56(Ba)

0.819

2.280

1.436

1 323

0 602

1.877

1.21

58(Ce)

0.789

2.316

1.596

1.305

0.641

1.901

1.21

60(Nd)

0.775

2.36

1.576

1.333

0.697

1.888

1.25

62(Sm)

0.768

2.33

1.659

1.320

0.747

1.849

1.26

64(Gd)

0.742

2.35

1.570

1.683

0.785

1.806

1.30

168

17 September 1973

PHYSICS LETI'ERS

Volume 46B, number 2

Table 1 (continued) 82 proton closed shell Z

80(Hg)

84(Po)

82(Pb)

N

E2

R4

E2

R4

E2

R4

R4(80)/R4(82)

116

0,426

2.49

1.063

1.529

0.668

1.915

1.30

118

0.412

2.546

1.026

1.450

0.677

1 84

1.38

120

0.368

2.574

0.961

1.439

0 686

1.75

1.47

126 proton closed shell N

124

126

128

Z

E2

R4

E2

R4

E2

R4

R4(124)/R4(128)

82(Pb)

0.803

2.10

-

-

0.795

1.38

1.52

are gT/2 and g9/2, respectively, that is, ]p ~ Jh [ 1 ]. With this guide line, we can predict that the symmetry nearly holds for the isotopes near Z = 28, but not for those near Z --- 82. The experimental data show that the prediction is really the case.

A regularity in the ratios Ra of the energy of the first 4 + level to that of the first 2 + level of closed shell +2 nuclei. The quantity R 4 has been known as one of the most ~mportant quantities to characterise the nuclear excitation behavior of the nucleus [ 2 - 5 ] . The single closed shell nuclei are considered as spherical and rather hard. The nucleus will soften if two nucleons are put on or removed from the closed shell. The softness or collectivity caused by this procedure can be measured by the quantity R 4 as discussed in ref. [5]. A compilation o f R 4 of closed shell nuclei and closed shell +2 nuclei f o r Z = 28, 50 and 82 and N = 28, 50, 82 and 126 is presented in table 1. In the last column is tabulated the quantity R 4 (closed shell - 2 ) / R 4 ( c l o s e d shell +2) which is a measure of relatwe softness for the nuclei with holes and particles. The following regularities can be observed in this table. 1) The quantittes m the last column are without exception larger than one. It implies that the nucleus with two holes is softer then the nucleus with two particles. 2) These values are remarkably constant m each nuclear region, that is, almost independent on the neutron or proton number in the unfilled shell. 3) This quantity increases as increasing mass member of treated nuclei. The B(E2) value of the gamma decay from the first 2 + level is another measure for the softness of

the nucleus. Unfortunately there exist only two pairs of single closed shell -+2 nuclei which have known B(E2) values, namely 50Cr26 (0.120) and 54Cr30(0.100) and 116Cd68(0.620) and l~0Te68 (0.55), where the figures in parentheses are B(E2) values in units of e2b 2. It is clear that the B(E2) of the nucleus with two holes is larger than that of the nucleus w~th two particles by the same order of magnitude as in the case o f R 4. Although theoretical explanations are not given to these regularities at the moment, they may suggest that the nucleus is much more likely to soften with prolate shape than with oblate shape and may provide the reason why prolate-shape nuclei are more frequently encountered :n the nature than oblateshape nuclei. The author is much indebted to Professors T. Marumori and N. Onishi for helpful theoretical discussions in the first part. He is also very grateful to Professor A. Bohr for his valuable and encouraging comment on the second part. References

ill M. Sakai, INS-J-136, Oct. 1972, Report of the Institute for Nuclear Study, University of Tokyo. [2] A. Bohr and B.R. Mottelson, Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. 27, No. 16 (1953). [3] G. Scharff-Goldhaber and J. Weneser, Phys. Rev. 98 (1955) 212. [4] A.S. Davydov and G.F. Filippov, Nucl. Phy~ 8 (1958) 237. [5] M.A.J. Mariscoth, G. Scharff-Goldhaber and B. Buck. Phys. Rev. 178 (1969) 1864. [6] M. Sakar, Nuclear Data Tables A10 (1972) 511. 169