Dynamical supersymmetry in 196Pt and 197Au

Volume 100B, number 5

PHYSICS LETTERS

16 April 1981

DYNAMICAL SUPERSYMMETRY IN 196pt AND 197Au J. VERVIER Institut de Physique Corpusculaire, B - 1348 Louvain-la Neuve, Belgium

Received 18 December 1980 Revised manuscript received 23 January 1981

The excitation energies, reduced E2 transition probabilities and spectroscopic factors in the (3He, d) reaction for the levels with positive parity in 197Au up to about 1 MeV, together with the corresponding data for 196pt, are shown to be in overall agreement with the predictions of a dynamical supersymmetry scheme recently proposed for nuclei in this mass region.

One of the major developments in nuclear spectroscopy during the last few years has been the Interacting Boson Model (IBM) [1,2] wherein the spectra of even-even nuclei are described as arising from s (L = 0) and d (L = 2) interacting bosons. The underlying group structure of the problem is the one of U(6). When the boson hamiltonian only contains Casimir operators of a complete chain of subgroups of U(6), analytical expressions can be found for its eigenvalues, which are labelled by the corresponding subgroups and their associated quantum numbers. Three analytical solutions exist in that way, denoted by SU(5), SU(3) and 0(6). Exanaples of experimental spectra corresponding to these three cases have been found, and in particular for 0(6) in the Os-Pt region [3], for instance in 196pt [4]. The extention of the IBM model to odd-mass nuclei has recently been investigated [5]. In this socalled Interacting Boson Fermion Model (IBFM), the three limiting cases of the IBM are also considered when studying the coupling of the fermion to the boson core. However, it is possible to find an analytical expression for the eigenvalues of the boson-fermion hamiltonian in the situation where the fermion is in one single orbit with angular momentum 3/2 and where the boson core is described by the 0(6) limit of the IBM [6]. The bosonic and fermionic degrees of freedom are then both included in one single theoretical framework, characterized by the group Spin (6),

and the hamiltonian is written in terms of the generators of Spin (6) (eq. (6.15) of ref. [2] ). Its analytical eigenvalues should describe the spectra of both the odd-mass nucleus and its even-even core. Moreover, the electromagnetic properties of the two nuclei should also be inserted in one unified description, together with the spectroscopic factors for the one-nucleon transfer reactions connecting them. The underlying symmetry of the system which includes the bosons and the fermion is called a dynamical supersymmetry. Examples of experimental spectra corresponding to this situation have recently been found in 192,194pt and 191,193Ir [ 6 - 8 ] . Extensive experimental data exist on the nucleus 197Au [ 9 - 1 2 ] , which may be considered as an e v e n even core, 196pt or 198Hg, plus a proton particle or a proton hole, which, in the ground state, is in the 2d3/2 shell model orbit. These data have often been interpreted in the framework of the core-particle coupling model [13], more specifically in the version of this model where only the first 0 + and 2 + levels of the core and the 2d3/2 orbit for the proton are taken into account [10,12,14,15]. In the most recent paper on this subject [12], it is shown that this model satisfactorily reproduces a large number of experimental data .on the magnetic dipole and electric quadrupole moments, M1 and E2 transition probabilities in this nucleus. It is the purpose of the present letter to show that the available experimental data on the excitation

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energies of the levels with assigned positive parity in 197Au up to about 1 MeV, on the E2 transition probabilities between them and on the spectroscopic factors for populating them in the (3He, d) reaction can also satisfactorily be described by the Interacting Boson Fermion Model, together with the corresponding data on 196pt. Use is made of the version of this model where the even-even boson core is described by the 0(6) limit of the IBM and where the odd fermion is in the 2d3/2 orbit [6]. These results then suggest the existence of a dynamical supersymmetry which links together the bosonic and fermionic degrees of freedom in these two nuclei. The analytical expressions for the theoretical energies of the levels in the bosonic and fermionic spectra for the presently considered model have been given by Iachello (eq. (7) of ref. [6] ). They are characterized by various quantum numbers which are defined in ref. (odd[6], i.e.: 01 ; 02 = 0 (even-even nucleus) or mass nucleus); 03 = 0 or 1 (same cases); r l ; r 2 = 0 or (same cases); vA ; and J, the angular momentum. Limits on the values of these quantum numbers are set by the number N of bosons, equal to 6 if the boson "core" is 196pt [4] and to 4 if it is 198Hg. These analytical expressions also include 3 parameters A, B and C, which are simply related to the coefficients of the expansion of the b o s o n - f e r m i o n hamiltonian in terms of the generators of Spin (6) (eq. (6.17) of ref. [2] ), and of which A splits the levels with different 01 . The experimental data on the nucleus 196pt are contained in the Nuclear Data Sheets [16], and the classification of its levels in terms of the quantum numbers o 1, r I and vzx has been proposed in ref. [4], wherein o = 01 and r = r I . The experimental data on the positive-parity states of the nucleus 197Au, ex-

16 April 1981

tracted from the above-mentioned references, include, 3 1 among other levels: the ground state 71 ; the first ~ 1, S l , 717 and 791 levels at 77.4,279.0,547.5 and 3 5 855.4 keV, respectively; the second 72, 72 and (~+ 2) states at 268.7, 502.6 and 736.7 keV, respec3 tively; the third g3 level at 1148 keV. These spin assignments are based on experiments, especially on (n, n'7) data [17,18] and on recent (3He, d) and Coulomb excitation studies [11,12] ; an exception is the state at 736.7 keV, which we have assumed to be 7+ , an hypothesis which is not contradicted by experiments but not imposed by them, and which fits into the present model. We have fitted the experimental excitation energies of the 8 levels in 196pt with assigned o 1 = 6 and 7"1 ~< 4 [4], and those of the above-mentioned states in 197Au (except -~3)to which we assign o 1 = ~ and 5 • r 1 <~ ~, 1.e. 15 experimental data altogether, by the theoretical expressions of ref. [6] with only 2 parameters B and C since we only include one value of o 1 in each nucleus. All experimental energies are assumed to have an uncertainty of -+0.1 keV, which determines their weights in the least squares fitting procedure. The resulting parameters B and C and the rms deviation s are given in table 1 (fit 1), and the calculated spectra are compared with the experimental data in fig. 1, wherein the values we assign for the quantum numbers o 1 and r 1 of the various levels are also given. The following comments can be made on these resuits. First, there is reasonable overall agreement between the experimental and calculated spectra as shown in fig. 1 : such a remark has already been made for 196pt [4] ; in 197Au, all the predicted levels with 5 o 1 = ~ and 7"1 ~ ~ are present in the experimental data at about their calculated positions, except the

Table 1 Parameters B and C (eq. (7) of ref. [6] ) and rms deviation s of the various fits to the experimental excitation energies of levels in 196pt and 197Au described in the text. B, C and s are in keV. See caption to fig. 1. Label

Data fitted

1

1 9 6 p t [ 2 ~ , 4+1 , 2 2+, 6 1+, 4 2 ,+ 3 1+, 0 2 ,+ 2 3+] 1+ 9+ 7+ 5+ 197.7 + . 5 +

C

s

2 7 6 -+ 2 4

17 +- 3.5

136

258 313 +-24 258

23 13 -+ 3.5 23

172 117 126

3+

2 3 4

a u t ¥ ~,~- ~,~ 1, 7 1, 7 2,~- 2,~- 2] 1 9 6 p t a) 1 9 6 p t b) 197Au c)

a) Ref.[4].

b) Dataoffit 1. C) Dataoffit. 1.

384

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CALC. (6, 3)

(4,0)

16 April 1981

EXP.

0"

196pt

6" (6,41 - (6,3)

2*

6; m2~

--q

4" (6,3) "

0;

--01 3"

--3; 4;

(6'2)

(6,3)

4"

(6,2)

(6,1}

2"

(6'0)

O"

~3 _5_,

11"

0÷

2"

2;

o;

CALC.

197Au

EXP

--9;

~2

Fig. 1. Comparison between the experimental [9-12, 16-18] and calculated (fit 1 of table 1) spectra of 196pt and 197Au. The indices on the experimental levels refer to their order of appearance; the quantum numbers (al, zl) for the theoretical ones are defined in ref. [6]. The 3'-ray branching ratios of the experimental states are indicated when known; the lines connecting the theoretical ones refer to large calculated E2 transition probabilities [2,6]. The E2 transition data on 196pt are not given since they have been discussed previously [ 3,4]. first ~+ 1 state which has so far not been localized. Second, the parameters we have obtained are similar to those adopted in ref. [4] in the framework o f the 0(6) limit o f the IBM applied to 196pt (table 1, fit 2); the small differences are partly due to a different choice o f the levels included in the fit. Third, the quality o f the fit obtained in ref. [4] for 196pt only (fig.2 o f ref. [4] ; rms deviation for all the states included: s

= 1 72 keV) is comparable to the one we get for 196pt and 197Au together (table 1, fit 1). Fourth, the present calculation reproduces the energy splitting o f the various levels and includes all the known positive-pail" ty states up to about 1 MeV in a unified description; this is not the case for the core-particle coupling model as it has been applied to 197Au [10,12,14,15]. To further investigate the second and third com385

Volume 100B, number 5

ments above, we have fitted the 8 levels o f 196pt included in our first calculation with the 2 parameters B and C. The results (table 1, fit 3) show that there is a good agreement between the two sets of parameters, for 196pt and 197Au together (fit 1) and for 196pt only (fit 3), and that the quality of the fit is not significantly improved when dealing with 196pt only. Finally, the 7 levels in 197Au included in our first calculation are satisfactorily reproduced by the parameters adopted in ref. [4] to fit experimental data on 196pt only (table 1, fit 4). Concerning the parameter A in the theoretical energies [6], its value can be deduced, in 196pt, from the excitation energy o f the third 0 + level at 1402.7 keV with assigned Ol = 4 and rl = 0 [4], and, in 197Au, . 3+ from the one o f the third 7 state at 1148 keV [11 ] a This yields A to which we assign Ol = ~1 and 71 = ~-. = 200 and 287 keV for 196Pt and 197Au, respectively. The average value A = 243.5 -+ 43.5 keV agrees reasonably well with the one adopted in ref. [4] for several levels with a 1 < 6 in 196pt only, i.e. A = 185 keV. A further test of the model can be found in the electromagnetic transition probabilities. That the comparison with the experimental data for the reduced E2 transition probabilities in 196pt is satisfactory for the 0(6) limit of the IBM has already been pointed out earlier [3,4] ; this conclusion can be immediately transposed to the IBFM considered here, and will not be elaborated further. In the lower left part of fig. 1, the calculated levels in 197 Au are connected by lines which denote large theoretical E2 transition probabilities [2,6]. The experimental branching ratios for the decay o f the various states in 197Au, indicated in the lower right part o f fig. 1, are in qualitative agreement 3 3 with the model, in particular the weak 7 2 - 7 1, 7 3 7 3 • 1 - ~ 1, 7 1 - 7 2 and 7 2 - 5.2 branchings, and the non-observation of the 7s 2 - 5.2, a 772 - 7 31, 772 - 5 .s2 , 9 1 - 7s 2 transitions. One exception 79 1 - - - ~ 2 and 5. $ 3 seems to be the large 7 2 - 7 1 branching; this however can at least qualitatively be explained by the large $ 3 M1 contribution to this 5 . 2 - 71 transition which can be deduced from the Coulomb excitation results of ref. [10] (82(E2/M1) ~< 0.04 from their angular distribution). We shall come back later to the E2 component o f this transition. A more quantitative test is to compare the reduced E2 transition probabilities in 196pt and 197Au calcu-

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lated with the expressions o f the model * i and the experimental data from Coulomb excitation [10,12,16] ; this is carried out in table 2. The overall agreement is seen to be satisfactory when considering 197Au only. 3 _ 1 In particular, the B(E2)'s for the rl = 7 to r 1 - 5. 3 3 1 and ~ 1 - 73 1 should all transitions, 7 1 - 5.1, 5s . 1 - 5. be equal since they do not depend on the spins but only on the number N of bosons and on the 7"1 quantum number (equations o f ref. [7] ); this is remarkably well verified experimentally, to within + 4%, from the data of ref. [10]. This equality is also predicted by the core-particle coupling model [13] if only the first 0 + and 2 + levels of the core are considered. The B(E2) for the 7a 2 - 5 -31 transition should cancel due to the A~"1 <~ 1 selection rule for E2 transitions [2] ; it is indeed ~:1 F. Iachello, private communication to the authors of ref. [7] (1980). Table 2 Comparison between the experimental [10,12,16,19] and calculated .1 reduced E2 transition probabilities B(E2) in 197Au, 196pt and 198Hg normalized to 1 for the average of the values 1+

3+

5+

3+

7+

3+

for the 5. 1- 5- 1, 7 1 - 7 1 and 5. 1-5. 1 transitions in 197Au"

Nucleus I i 197Au

If

B(E2) B(E2) (calc.) (exp.)a)

B(E2) (exp.)b)

71 + 1 73 +1

1

0.99 ± 0.11

1.19 -+0.12

3

5+

3+

7 1 7 1

1

0.97 -+0.06

0.98 -+0.17

1

rf = 7

7+

3+

¥ 1 7 1

1

1.04 -+0.05 0.83 -+0.04

197Au

73 + 2 73 + 1

0

0.38 +-0.03

ri=7

5

~'i = 7 1

5+

3+

7+

3+

7 2 7 1 0

0.44 -+0.11

<0.001

-

~<0.001

-

rf = 7

7 2 7 1

0

197Au

73 + 2 71 + 1

1.30

0.64 +-0.13

0.65 -+0.11

1.30

-

0.82 +-0.36

1.30

-

0.23

0.006 ± 0.002

5

9+

5+

7 1 7 1

3

11 +.

7+

7+ 7 1

5+ 5. 1

7+

3+

ri= 7

rf= 7 197Au 3

5" 1 7 1

0 . 0 0 5 -+ 0 . 0 0 2

ri= 7 rf = 73

7 1 7 2 ~+ 1 71+ 1

0

0.22 -+0.07 0.17 -+0.05

0

0.53 +-0.10

0.54 -+0.12

196pt

27

07

0.91

1.32 -+0.07

1.55 -+0.09

27

07

0.89

0.97 -+0.04

1.14 -+0.05

t98Hg

a) R e f . [ 1 0 ] f o r 1 9 7 A u .

b) Ref. [12] for 197Au.

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reduced, by a factor of about 2.5, in the experimental 1 5 7 data with respect to the ~- 1, ~- 1 and ~ 1 states. In the core-particle coupling model, this reduction is explained by an "ad hoc" mixing between the 31 and 32 levels [14]. The same Ar 1 ~< 1 selection rule is seen to be very effective in reducing the B(E2)'s for 5 3 7 the r 1 = ~to r 1 = 2I transitions, 25 2 - 21 and ~2 - ~3 1, whose approximate experimental values can be deduced from the data of ref. [10] (see the note added in proof in ref. [10] ). Concerning the B(E2)'s for the 5 3 r 1 = ~ to r 1 = ~- transitions, the only ones experimenS tally known are 3 2 - ½1 and ~9 1 - 21 ; the former is a factor of 2 too small, and the latter agrees with the model, although with a large experimental uncertainty 3 [12]. For the A~-1 = 0 transitions within the r 1 = 7 S multiplet, only ~_1 - ~ 1 is allowed and its experimental value is a factor of 4 smaller than the calculated one; 71 3 2 a n d ~s 1 - ~2 3 E2 transitions the forbidden ~are reduced, by factors of about 5 and 2, respectively, with respect to the average B(E2) for the ~ 1 - ~ 1a, ~ 3 1 _ 3 ~-1 and ~-1-~-1 7 a transitions taken as unity in table 2~ In summary, table 2 shows that the model accounts reasonably well for the reduced E2 transition probabilities in the nucleus 197Au, with however some points of discrepancy. It should be noticed that this agreement only relies on the quantum numbers N and r 1 assigned to the levels, and does not depend on the fit to the excitation energies represented by the parameters A, B and C obtained above. When dealing with 196pt, it has been noticed before [3,4] that there is a good agreement for the relative B(E2)'s within this nucleus, also independent o f the fit to the excitation energies, and it is not displayed in table 2. However, the absolute value ofB(E2, 2 1 - 0 1 ) is about a factor of 1.6 too large with respect to what would be predicted from the experimental data in 197Au, as shown in table 2. This would indicate that the value of the overall normalization constant a in the theoretical B(E2)'s (equations of ref. [7] ) is not the same in 196pt and 197Au, suggesting a different "deformability" for these 2 nuclei, or a breakdown of the b o s o n - f e r m i o n supersymmetry for the E2 transitions between their levels. Another explanation could be that the o 1 quantum number we have assigned to the low-lying levels in 197Au, i.e. 01 = ~ (fig. 1), should be modified to o 1 = 9 (corresponding to a number of bosons N = 4 in 197Au); in this case, the calculated B(E2, 2 1 - 0 1 ) in 196pt would become 1.66 in the

16 April 1981

units of table 2, i.e. close to the experimental value (table 2). Another test of the model arises from the spectroscopic factors in the one-nucleon transfer reactions connecting the boson and fermion systems [8], i.e. the 196pt (3He, d)197Au reaction in the present case. The comparison between the experimental data [11 ] and what can be calculated from the model ,2 is carried out in table 3. Starting from the 196pt ground state with assigned quantum numbers (Ol, r l ) = (6, 0) [4], the allowed transitions in this reaction 1 should obey the selection rules Aa 1 = + $- and Ar 1 = + ! ,2 The experimental data indeed show that these selection rules suppress the transitions to s 1, 1, ~-2 7 and ~9 lbelow the level of detection in the experiment [11 ], and reduces the transitions to 3 2 by a factor of about 2.5. They also indicate that ½1 and if2 include sizable contributions o f t h e 3 S l / 2 and 2d5/2 proton orbits, respectively, and that ~3 receives a population about twice too low with respect to the predictions of the model. This test of the model is also independent of the fit to the excitation energies. Finally, we have also investigated the hypothesis ,2 F. Iachello, private communication to the authors of ref. [81 (1980). Table 3 Comparison between the experimental [11 ] and calculated ,2 spectroscopic factors C2S (normalized to 1 for the 197Au ground state) in the 196pt(3He, d)197Au reaction. See caption to fig. 1. Level 3+

1

1+

~- 1 5+

~- l

(e 1, r 1) 13

1

3

0.89

0

3

not seen

0

3

not seen

0

0.40

0

0.34

0

not seen

0

not seen

0

0.27

0.6

( ~ , ~) (~, ~)

7+

1 3+ ~- 2

(~', ~) (~, s ~-)

s+

(~

~- 2 7+

~- 2 9+ 1 3+

)- 3

5

--, ~-) S

( ~ , ~-) (~, 5 ~-) 1

( ~ , $-)

a)

C2S(~alc.)

1

(~-, ~-)

13

C2S (exp.)

1 a)

a) Normalised, 387

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that 197Au can be considered as a 198Hg boson core plus a proton hole in the 2d3/2 shell model orbit, as is suggested by Bolotin et al. [12] from the core-particle coupling model, and in agreement with the fact that the number of bosons in the Pt region is determined from the number of holes in the Z = 8 2 , N = 126 closed shells. Without giving much details about these calculations, we may state the main conclusions. The applicability of the 0(6) limit of the IBM to 198Hg is much less established than to 196pt. The rms deviations of the fits one gets to the levels of 198Hg and 197 Au together in the dynamical supersymmetry scheme are much worse (by factors of about 2) than for 196pt and 197Au together, and for 198Hg alone. The parameters of the fits for 198Hg alone, and for 198 Hg and 197 Au together, are significantly different. The reduced E2 transition probability B(E2, 2 1 - 0 1 ) in 198Hg [19] is in better agreement with the corresponding data in 197Au than the one in 196pt (table 2). There are no available data on the 198Hg(d, 3He)197Au one-proton pick up reaction. In conclusion, we have shown in the present letter that the experimental data available on the positive parity levels in 197Au up to about 1 MeV, together with the corresponding states in 196pt, can be fitted in a unified way in the framework of a boson-fermion hamiltonian with a dynamical supersymmetry, suggested to e.xist in this region by Iachello [6], which links together the properties of the boson "core" 196pt and of the fermion "system" 197Au. The quality of the fits obtained for the excitation energies, the reduced E2 transition probabilities and the spectroscopic factors for one-proton transfer reaction is at least comparable to the ones achieved for 196pt assuming a dynamical symmetry for the boson hamiltonian

388

16 April 1981

[3,4] and for 192,194pt and 191,193Ir with a dynamical supersymmetry [7,8]. Further extentions of this work include: from the experimental side, the location of other levels predicted by the model and the determination of their properties, for instance the missing ~- 1 state of the 5 r 1 = 7 multiplet predicted to be around 1100 keV with the parameters of fit 1 in table 3; from the theoretical side, the extention of the IBFM model to include other proton orbits than 2d3/2, like lh9/2 and others, as is now being carried out in 185-195Au [20].

References [1 ] F. Iachello, ed., Interacting bosons in nuclear physics (Plenum, New York, 1979), and references therein. [2] O. Scholten, The interacting boson approximation model and applications, Ph.D. thesis (Dijkstra, Groningen, 1980), and references therein. [3] R.F. Casten, in: Interacting bosons in nuclear physics, ed. F. Iachello (Plenum, New York, 1979) p. 37. [4] J.A. Cizewski et al., Phys. Rev. Lett. 40 (1978) 167. [5] F. IacheUo, Nucl. Phys. A347 (1980) 51. [6] F. Iachello, Phys. Rev. Lett. 44 (1980) 772. [7] M.N. Harakeh et al., Phys. Lett. 97B (1980) 21. [8] Y. Iwasaki et al., to be published. [9] B. Harmatz, Nucl. Data Sheets 20 (1977) 73, and references therein. [10] F.K. McGowan et al., Ann. Phys. (NY) 63 (1971) 549. [11 ] M.L. Munger and R.J. Peterson, Nucl. Phys. A303 (1978) 199. [12] H.H. Bolotin et al., Nucl. Phys. A321 (1979) 231. [13] A. de-Shalit, Phys. Rev. 122 (1961) 1530. [14] A. Braunstein and A. de-Shalit, Phys. Lett. 1 (1962) 264. [15] A. de-Shalit, Phys. Lett. 15 (1965) 170. [16] J. Halperin, Nucl. Data Sheets 28 (1979) 485. [17] J.A. Nelson et al., Phys. Rev. C3 (1971) 307. [18] E. Barnard et al., Nucl. Phys. A167 (1971) 511. [19] B. Harmatz, Nucl. Data Sheets 21 (1977) 377. [20] J.L. Wood, Bull. Am.Phys. Soc. 25 (1980) 573,740.