The level structure of the 153Gd nucleus studied in the 150Sm(α, n)153Gd reaction

Nuclear Physics A371 (1981) 364-380 © North-Holland Publishing Company

THE LEVEL STRUCTURE OF THE ' s3 Gd NUCLEUS STUDIED IN THE "° Sat(a, n)' s3 Gd REACTION J . REKSTAD, P. BQE, A. HENRIQUEZ, R . QYAN, M . GUTTORMSEN and T . ENGELAND

Inslilule gjPhrsics, Unirersilr q(O.s/o, O.s/o, Norxwr and G . LQVHQIDEN

Inslifulc~ q/ P/arsics, Unioc"rsitr q(Bergen, Bergen, Nnrwur Received 9 June 1981 (Rcviscd IOAugust 1981) A6atract : The level structure of "'Gd has been studied by means of the "°Sm(a, n)"'Gd reaction . The experiment included measurements of }" -," coincidences, ~" -angular distributions, }~-ray yield at 17 MeV and 19 MeV beam energy, and ~"-ray multiplicities . Favoured and unfavoured members of the positive-parity i  , Z band were identified . States belonging to the h  , z and f,, Z band structures have been lordted . Surprisingly low multiplicity numbers were deduced for ' ° 'Gd ;-rays . This may indicate that the (a, n) reaction is not a pure compound reaction . The level structure of' s 'Gd has been compared to the known structure of other odd-mass N = 89 nuclei, and a close similarity is found . The positive-parity band structure has been compared to calculations with the pairing-plus-recoil model . Good agreement is obtained without any ucl hnc Coriolis attenuation. E

NUCLEAR REACTION " ° Sm(x, n), E = 17, 19 MeV ; measured EÏ, 1. ., ~;-coin, ~" -multiplicities . ' s'Gd deduced levels, J, n, K . Enriched target . Ge(Li) and iVal detectors.

1 . Introduction The odd-mass N = 89 isotones are considered to define the low-mass border of the rare-earth deformed region, and attempts to describe the nuclear structure in terms of the standard approach of the particle-rotor model appeared to exhibit severe shortcomings for the N = 89 nuclei, Recent studies t ~ a) of the t s t Sm nucleus in terms of more sophisticated versions of the particle-rotor model with an explicit inclusion of the recoil term have shown that the general structure may indeed be accounted for by the degrees of freedom considered in this model. To achieve an even better quantitative agreement with the experimental data it seems necessary to introduce a microscopic treatment of the interactions between several valence particles. Such a model has been proposed in recent papers a, a), and represents an extension of the conceptually simple particle-rotor model . Whereas the nucleus t s' Sm is well studied t " z ' s - t a), information on the other N = 89 isotones is more scarce . In the present study the low- and intermediate 364

365

J. Rekstad et al. / The leoel structure

spin states in 's 3Gd have been investigated with the 's°Sm(a, ny) reaction . This nuclide has been studied by means of various experimental techniques ' a. z4), and e.g. favoured spin states of the i~ positive-parity band and the -(505) band were observed and understood at an early stage ' e . Z°) . However, many problems concerning other negative-parity states and unfavoured spin members of the i,~ bands have remained unsolved . Such non-yrast states carry very important and relevant information for model descriptions of the nuclear structure, and should be more favourably studied in the (a, n) reactions where less angular momentum is transferred to the compound system than in the (HI, xn) reactions. 2. Experimental method The experiments were performed with 17 MeV and 19 MeV a-beams from the FN tandem accelerator at the Niets Bohr Institute. The 2.9 mg/cm 2 thick self-supporting' s°Sm target was isotopically enriched to approximately 96 %. With these beam energies two competing reactions take place ;the (a, 2n) and the (a, n) reactions are about equally strong . In order to separate the y-radiation from the two reactions a many-detector multiplicity arrangement was used. Four Ge(Li) detectors were placed at 0°, 90° and ± 125° with respect to the beam . The efficiency of the multipli-

1100

1200

1300

îf00 1500 1600 17170 CHANNEL NUMBER

1800

1900

X00

Fig. I . A two-fold spectrum from the bombardment of ' °°Sm with 19 MeV a-particles. The spectrum is recorded at an angle of 90° relative to the beam .

366

J. Rek.stadet al . I The lel"el .structure

city filter was increased by the inclusion of three Nal counters placed at ±55° and 120° . The y-y coincidence events from two Ge(Li) counters were recorded on tape for fold >_ 2 with the requirement that at least two of the y-rays were detected in Ge(Li) counters . With fotir Ge(Li) counters it was possible to create 12 statistically independent y-y coincidence spectra. These were added together . A two-fold projection spectrum from the 19 MeV run is shown in fig. 1 . Energies and intensities for the y-ray transitions obtained from a singles spectrum taken in 55°, and with the same beam energy, are given in table 1 . TANLI: I Gamma rays from the bombardment of ""Sm with 19 McV a-particles /. .(19McV)

Transition

/~ (17 MeV ) 93 .3 109.8 126.1 129.1 141 .9 145.5

10 .5(12) 40 .3(22) 41 .1(39) 1 .9113) 12 .0113) 17 .1(19)

-0 .19(10) -0 .31 (9)

0.39(13) -0 .21(10)

-0 .05(20)

-0 .19121)

2.5 0.9 2.3 1 .2 I .0 5.1

174.4`)

57 .1(30)

0.00(75)

-0.26(10)

1 .4 (1)

178.0

16.6(46)

1 .1 (2)

183.3 `)

16 .0114)

0.9 ( I )

192.3 195.1 197.1

72 .0(31) 31 .3(34) 98 .6(69)

-0.42 (8) 't?.26(15) - 1 .31(21)

-0 .20 (9) 0.01116) 1 .14(23)

4.0 (3) 0.9 (1) 0.5 (1)

211 .7 `)

37 .1(28)

- 0.42(12)

- 0.20(401

2.6 (2)

100.0(90) 9.6(IR) 54.2(70) 29 .5(47) 7.6(22) 18 .6(29)

0.29 (5)

-0.23 (5)

0.23(11)

0.02(12)

0.57 ( I )

0.07 (1)

6.0 (5) 6 .0(11) 2.6 (4) 2.0 (3)

32 .1(28)

-0 .20(15)

0.07(14)

18 .4(23) 13 .3(21) 10 .1(22) 13 .3(18) 9.4(19) 21 .4(20) 11 .0(20) 9.5(30)

0.04(20) 0.18(27)

-0.30(22) - 0.30(30)

1 .5 (1) 2.7 (5)

0.41(24) -0.18(35) 0.23(IS) 0.01(30)

-0 .23(24) 0.18(37) - O.18(18) - 0.65(64)

2.4 (2) 2.l (1) 2.1 (2) 2.5 (3) 1 .2(13)

0.36(35)

0.09(37)

1 .1 (4)

226.3 229.7 238.8 239 .9 245.9 247.4 249.5 `) 271 .4 275.2 279.1 282.3 285 .5`) 291 .6 298.4 303.4 `) (301 .9 and 303.5) 315.E

9.6(24)

(4) (1) (1) (9) (1) (4)

4.3 (8)

93 .3 -~ 109.8 -. 219.4-. 129.1 -+

0 0 93 .3 0

~ 215.9--~ 1303 .5 -" 219.4 -. : 183.3 ~ I. 395.3 ~ 363.5-~ =""Po '"F ( 575.2 -. ~. 212.1 -. 361 .0 -. 804.9 -. 769.4 -. 333.2 -~ 1050 .8 --. 550.9 ~ 610 .5 ~ 972.5 ~

41 .5 129 .1 41 .5 0 212 .1 171 .2

1i

363.5 0 134.7 572.2 530.E 93 .3 804.9 303.5 361 .0 723.7

674.4 ~ 395.3 812.9--.530 .E 395.3 ~ 109.8 333.2 ~ 41 .5 514.3 -~ 215 .9 395.3 -. 93 .3 303.5 -~ 0 0 315.6 -+

367

J. Rek.stad et al. / The lerel .structure TABLI: I (continued)

E.,(kcV)')

lï

320 .0 327 .2

7 .6131) 8 .1(24)

ti)

Az

A,

1 . . (19 MeV) /I. (17 MeV) 1 .1 (21 I .5 (?)

Transition

497 .0(44)

0 .04 ( I )

-0 .10 (2)

I .I ( I )

41 .4(35)

0 .29(14)

- 0 .33(IS)

4 .3(12)

502 .0140)

0 .25 (2)

- 0 .14 (2)

i sas m ~ R98 .7 -. 564.E 887 .E ~ 550 .9 i SzGd ~ 564.E -+ 219 .4 ~SZGd

351 .7

ll .l(14)

0 .22(21)

- 0 .01(24)

362 .7 `)

23 .4(21)

0 .29(14)

-0 .25(I5)

4 .2

367.7 383 .1 `) 386.0 411 .0 419.4 421 .8 427.0 439.5 441 .4 445 .5 466.9 471 .9

5 .7(18) 9 .0(42) 4.4 (7) 221 .3(26) 6.8(31) 5 .0(25) 5 .9(21) 12 .9(20) 7 .1135) 7 .5(14) 3 .3(15) 53 .5(19)

723 .7 ~ 361 .0 ~ 972 .5 ~ 610 .5 1034.8 -+ 674 .4

475 .9 `)

19 .7(13)

489 .1 496 .5 519 .E 526 .8 537 .3 540 .5 586 .2 611 .7 627 .5 638 .1 650 .5 693 .5 709 .0 943 .5

10 .8(35) 0 .3 (2) 5 .6(16) 16 .7(13) 7 .6(12) 5 .0(15) 36 .4(16) 6 .3(25) 1 .1 (7) 8 .0(16) 12 .3(45) 34 .8(99) 67 .3(33) 4 .6(22)

334 .0 `) 336.7 344.4 `)

0 .45(19) 0 .30 (3)

0.32(21) - 0.19 (3)

2 .4 (3) 4 .4 (6) 8 .3(14) 14 .3(10)

716 .4 -. 333 .2 'S=Gd 'SzGd 1318 .1 -. 898 .7 550 .9 -. 129 .1 ' S'Gd ' S zGd 804 .9 ~ 363 .5 1010 .1 -+ 564 .E 1190 .6-.723 .7 'S=Gd

3 .0 16) 0 .27(23)

0.05(23)

0 .37(39)

- 0.37(36)

0 .34 (7)

- 0.19 (9)

13 .3(IS)

0.571121

- 0.06(12)

4 .8 (5)

2 .3 (2) 2 .4 (3)

1 .9 (3) 0 .20 (5) - 0 .49(19) 0 .57(4R)

- 0.13 (6) 0.18(20) - 0 .47(53)

- 0 .25(15)

- 0 .01(16)

0 .72(10)

0 .30(ll)

6.2(IR) 5 .7 (7j 2 .4 (4) 0.8 (I) 1 .0(70) 2 .2 (4) 2 .9 (7) 1 .7 (4) 0.8 (2)

~

610 .5 -. 134 .7 1050 .8 ~ 575 .2 530 .6 -. 41 .5 'SzGd 'SzGd 'SzGd

972 .5 ~ 361 .0 821 .4 ~ 193 .3 1472 .0 ~ 821 .4

') The uncertainty in energy is 0 .1 keV . n) The intensity of the 226.3 keV transition is 100 . `) The peak is a doublet or a triplet .

The yield ratios IY(19 Mew/lY(17 Mew are also given in table 1 . In general this ratio is much larger for y-transitions following the 2n reaction than for those originating from the In reaction, but it depends also on the spin of the de-exciting level. The relative y-ray intensities in 0° and 90°, also given in table 1, are extracted

368

J. Rekslad et ul. / The level .structure

from the projection spectra. Although the multiplicity of a transition and the multipolarities of other transitions in the cascade may influence this ratio. Typically, we find IP~o ;(0°)/IP~o~(90°) > 1 .3 for quadrupole transitions and < 0.6 for dipole transitions . Thus, the in-band transitions are in general easily identified . The ~~-y coincidence experiment was performed with a 19 MeV a-beam . Gates were put on all significant y-ray lines, and the resulting coincidence spectra for some of the selected gates are shown in fig. 2 . Finally, the relative y-ray multiplicities were determined from the yields in the singles spectrum and the projection spectra with different fold numbers.

N FZ

Gat.

zse .a

Gate

382.7 " 381 .8 " 81 .<

Gat~

7e3 .1 " 3er.r.

r~

O ca W O

~" ~ l'fZrbi~

W m Z

CHANNEL NUMBER

500 700 400 600 CHANNEL NUMBER

900

Fig. 2. Coincidence spectra with gates put on some selected transitions in the 'S'Gd nucleus.

J . Rekstad et al. / The leue! structure

36 9

m zo_

F Ci W N O a_ V

W Z C9 K W z W

Fig. 3. The observed band patterns in ' °ZGd and 's'Gd. The two decay schemes are drawn in a correct energy scale with the ground state in 's'Gd as zero . The widths of the arrows represent the intensities of the transitions. At the top are shown the intensity distributions versus spin for the two channels, compared to an optical-model calculation of the cross section fordifferent angular momentum transferred in the compound reaction .

3. A comparison of the (a, o) and (a, 2n) reactions The observed band patterns in ts2Gd and ts3Gd are shown in fig. 3, where the transitions are drawn in an energy versus spin diagram with a correct reaction

J. Reksrad et al. / The le~~el structure

37 0

energy scale. At the top of the figure are shown the intensity distributions with spin for the two reaction channels, adopted from the measured y-ray intensities. It follows that most of the strength in the 2n channel is taken from the low-spin part of the available compound reaction cross section, resulting in a positive skewness as defined in ref. z') . The 1 n distribution is much broader and has a negative skewness as shown in fig. 3. The ground band in ' szGd is observed up to approximately the maximum value for energy and spin allowed in the reaction . It is surprising that such an amount of the total compound reaction cross section is carried by the 2n channel since the tszGd nucleus is entered in a region with a very low level density (below 2 MeV). In ' s3Gd one observes bands up to about 1 .2 MeV in excitation energy . There remains an energy of about 7 .5 MeV from the highest observed level to the energy of the compound system . This energy gap must be accounted for by the emitted neutron and by the Y-rays not observed as discrete lines in the spectrum . In order to estimate the number of y-rays in the decay, the ratios between the intensities of the transitions in the three-fold, two-fold, and singles spectra were deduced. A careful multiplicity calibration of the spectrometer was carried out by means of a tszEu source . The ratio between the intensity of a specific y-transition with energy E., in the two-fold and the singles spectrum is proportional to (M-1) (M-2~(EY ), where M is the multiplicity and J(E},) is the probability for detecting in a Ge(Li) counter one of the y-rays in coincidence with the transition Ey, . In principle one has to measure the energy and intensity of all the transitions in coincidence with EÏ in order to determine M from this ratio. In 'szGd only a small amount of energy is available in addition to the energy ofthe transitions seen as discrete lines in the spectrum . Thus, it is possible to determine TABLE Z

Gamma-ray multiplicitics for some transitions in ' SZGd and "'Gd Er (keV) 344 41 I 472 519 226 362 192 211 229 E, = 19 MeV .

M

/.. (3-fold) lï (2-fold)

2 .6 2 .? 3 .1 4 .3

(0 .1) (0 .1) (0 .2) (0 .7)

0.15 0 .17 0 .21 0 .31

(0 .03) (0 .03) (0 .04) (0 .07)

szGd

3 .4 3 .7 3 .4 3 .4 3 .5

(O .l) (0 .3) (0 .2) (0 .3) (0.4)

0 .20 0 .22 0 .19 0 .20 0 .21

(0 .03) (0 .03) (0 .04) (0 .04) (0 .05)

's'Gd

Transition 2+ 4+ 6+ 8+

L+ z ~+ z u_ z

~ -+ -. ~

0+ 2+ 4+ 6+

~+

+ ~ ;i z_ yu

N ucleus

J. ReA.ctad et al. / The lerel .siructure

371

accurate values for the multiplicities in `sZGd from an analysis of the observed cascades. The results are given in table 2. The multiplicities are expected to be generally larger in 's3Gd than in 'sZGd since the ' s3 Gd nucleus presumably is formed at a much larger excitation energy than ` sZ Gd. Based on the known cascades, the multiplicities of the transitions in is3Gd were evaluated in a similar manner as for' sZ Gd. The results, given in table 2, show that the deduced multiplicities are small, and not significantly larger than for the ground band in ` sZ Gd. Since the total efficiency of the Ge(Li) counter is energy dependent one may obtain a too low value for the multiplicity with this method if the cascade contains many y-rays with high energies . In order to eliminate this uncertainty we also cal-, culated the ratios between the three-fold and two-fold y-intensities. The three-fold spectrum is generated essentially by the inclusion of one additional NaI counter to the configuration responsible for the two-fold spectrum . Thus, the ratio between the three-fold and two-fold intensities is proportional to M-3, and nearly independent of the y-energies . In table 2 these ratios are compared for some transitions in ` sZ Gd and `s 3 Gd. The values are about similar for the two nuclei, and we get no support for a conclusion that ' s3 Gd has larger multiplicities than 'sZGd. These results seem to indicate that under the given conditions a considerable amount of the energy involved in the (a, n) reaction, approximately (~7 MeV, is carried by the neutron. This is significantly above the energy expected in a pure evaporation process. Thus, the entry states occur low in excitation energy which explains the low multiplicities found for the 's 3 Gd nucleus. 4. Uiseussion of levels in ' s3Gd The states with higher spin than those which can be reached in single neutron transfer, are known from the early investigation of the 'sZSm(a, 3n)' s3 Gd reaction ' 9 . Z°). The following discussion is based on the results obtained in the present study of the 's°Sm(a, n)`s3Gd reaction together with the bulk of information presented in previous experimental investigations' s-Z3 ). The decay scheme of ` s3 Gd is shown in fig. 4 where the levels have been sorted in a band pattern according to an interpretation in terms of the particle-rotor model . All together 19 new levels have been suggested as a result of the present experiment . The evidence for these suggestions is given in the following discussion of the different band structures . 4 .1 . THE u - (505) BAND

The strongly coupled L2 = z band is observed in all the odd-neutron nuclei in this mass region, and it occurs as a well-behaved rotational band even in the N = 87 transitional nuclei . The band members up to spin have been populated

J. Rekstad et al. / The lerel .struc "ture

372

u u

N

d U C

ôi p~ nv

IV IN 7 ~o ~ow

L-I_IJ~L

ö

~~r~

C

~r~~"~

N

a.

T

3 N

N V

3

~4

O n

8

n

n

~

~

n

~

~

~

n

8

(A~H) A'Jä3N3 NOIldlI~X3

n

n

~

v

J. Rekstad et al. l The level structure

373

in the (a, n) reaction, and the lowest transitions in the band appear as some of the strongest y-ray lines in the spectrum . The spectrum in coincidence with the 192.3 keV line is shown in fig. 2. Our results confirm the assignments given in refs. 1s-ZO). 4 .2 . THE

î,3 .z

BAND STRUCTURE

The decoupled band structure associated with the i13î2 single-particle state is also a characteristic feature of the odd-mass nuclei in the A = 150 mass region . The 226.3 keV transition is one of the strongest y-ray lines in the spectrum and represents the lowest transition z + -" + in this yrast cascade. The decoupled band which constitutes the favoured branch of the îl3/2 band structure is populated to spin i+ and agrees with the interpretation given in refs. ' 9 . Zo) . Two strong y-ray lines with energies 362.7 keV and 249.5 keV respectively are seen in coincidence with the 226 .3 keV transition (fig . 2). The 362.7 keV transition is the ~-+ -~ i+ member of the decoupled band ' 9 . Zo), while the 249.5 keV line is about equally strong and belongs to the unfavoured branch consisting of the sequence of states i+, i+, i +, . .. The 249.5 keV peak is a doublet with the + -. 1i + transition as the main component. This interpretation agrees with the dipole character of the radiation. Thus, the -~+ state occurs at 610.5 keV in disagreement with the suggestion given in ref. 2°). The second component of the doublet has an energy of 248.9 keV, and is interpreted as the + -> i+ transition . This transition is seen in coincidence with the 362.7 keV line, which actually is a triplet, but with ~+ -~ u+ as the dominating component. We also observe a 611 .7 keV transition in coincidence with 226.3 keV, which corresponds to the energy sum 362.7 keV+248 .9 keV. Thus the energy of the + state is 972.5 keV. 4 .3 . THE h9,z BAND STRUCTURE

In the neighbouring isotone 1 s 1Sm a partly decoupled h~ band was identified in the study of Guttormsen et a1.2). A similar band structure is located in the present work, and fig. 4 shows this band with energies and spins consistent with all available information from the coincidence measurements, angular distributions and the IY(19 MeV)/IY(17 MeV) intensity ratios . The assignments are also consistent with previous transfer data. The suggested ?-, ~- and ~- members of the band are connected with quadrupole transitions of 445.5 keV and 345 .2 keV. Also the 298.4 keV transition between the~- and the ~- members ofthe band is ofquadrupole type . Furthermore, the 126.1 keV transition from the ~- state at 219.4 keV to the 93.3 keV level (~-) is of dipole type . The transitions to the known ' s) ~- and ~states at 109.8 keV and 129.1 keV had too low y-energy to be detected in the present experiment . The suggestion of a ~- and ~- state at 215.9 keV and 219 .4 keV respectively is

374

J . Rekstad et al . l The lese! structure

1400

64

,.,1200 s Y Y 1000

89

/

bytz band

/ /

C)

n

W 2 W 2 O_ F Q

~- 400 U W

0 Y2

~z

9h Wt SPIN (h )

nlz ~lz

i

Vz

i

~2

i

I i0

9/z ~/z SPIN (fi)

.5i

n/z

. Sb tA i

r/2

Fig. 5 . A comparison of the h ,~ bands in '"Gd and 's'Sm . For the nuclear structure factors see the discussion in the text .

also consistent with available transfer data, as it offers an explanation for the apparently strong (d, p) population of the ~ ~ + (402) state at 212 keV [refs. te.22)] . This is a hole state in the N = 89 isotones and in t s t Sm it is at most very weakly populated in the stripping reaction') . Thus the (d, p) stripping strength ascribed to the ~ ~+(402) state in tssGd most probably has to be associated with other levels . The (d, p) cross sections of the analogous ~- and ~- states in t st Sm are 92 and 16 pb/sr (at 45°) and the sum is consistent with the (d, p) cross section for the 217 keV level in t s a Gd observed by Tj~m and Elbek ' 6 ) . By assuming that the (d, p) cross section measured for the 217 keV particle group in tssGd is shared between the ~- and ~- states in the same way as observed for t s t Sm, it is possible to deduce nuclear structure factors for the states . These are displayed in fig. 5, where a comparison is made of the suggested ht band in ts3Gd with the established band in t s t Sm. The remarkable similarity lends further support to the assignments put forward in the present work. 4 .4 . THE

f, ;Z

BAND STRUCTURE

Based on the information from the coincidence measurements we suggest the band structure labelled f~ in fig. 4. The ~- and ~- states are known from previous investigations ts. t'), and the angular distributions and the IY(19 MeV)/IY(17 MeV) intensity ratios for the 239.9, 291 .6 and 383.1 keV transitions give evidence for the ~- and z- assignments of the 333.2 and 716.4 keV levels .

J. Rekstad et al. / The level structure

37 5

4.5 . OTHER LEVELS

The levels to the right in fig. 4 are established from the coincidence data. The levels below 395.3 keV are known 1 s) from previous studies. The suggested spin values are based on the measured angular distributions and the Iy(19 MeV)/lY(17 MeV) intensity ratios . The 530.6 keV level is probably identical to the ~- state populated previously in the (p, t) reaction 21) . 5. The nuclear structure of the N = 89 isotopes ; comparison with particle-rotor model calculations

The close similarity between the bands in 1 s3Gd and 1 s 1 Sm was discussed in subsect. 4.3. This is indeed quite general, as can be seen in fig. 6 where the level scheme of 1s3Gd is compared with the known structure of's 1 Sm and 1ssDy . Only the four characteristic band patterns originated from the i- (505) Nilsson state and the Coriolis coupled h~, f~ and i13î2 intrinsic states are shown. The strong similarity between these bands for the various N = 89 isotopes supports the idea that these transitional nuclei exhibit features that are mainly governed by the number of neutrons outside the N = 82 closed core . 5 .1 . DISCUSSION OF THE NEGATIVE-PARITY STATES

The negative-~rity states in an odd-mass N = 89 nucleus were for the first time given an appropriate description in the paper of Guttormsen et al. 2). Due to the similarity in structure of the N = 89 isotopes this calculation, which was carried out for l s l Sm, is suitable for the other nuclei as well, as can be seen in fig. 6. Details of the calculation, which is based on an axial symmetric rotor with an appropriate single-particle level scheme of the Nilsson type and with all rotational degrees of freedom included, are given in ref. 2). Also shown in fig. 6 are the positive-parity states resulting from a new calculation described in detail in subsect. 5.2. Except for the strongly coupled u- (505) band found in all these nuclei, the rotational properties are partly masked due to strong Coriolis perturbation . The characteristic features of the f~ and h~ bands are reproduced in the calculation. These results depend strongly on the intrinsic Nilsson energies and wave functions 3). The most striking difference between the level schemes of the three nuclei is the change in the f~ band . Both in 1s3Gd and 1ssDy the three lowest states with spin ~-, ~- and ~- are nearly equally spaced in good agreement with the calculation, whereas in 1s1Sm the ~- and ~- states are close in energy with the }- state as the ground state. In ref. 2) this abnormal behaviour in 1s1Sm was explained as Coriolis coupling to the low-lying Qx = ~- orbital of f~, nature which could push the ~ground state down in energy . This could not be reproduced by the model without making an adjustment of the intrinsic Nilsson energy for the ll~ _ ~- orbital.

376

J. Rekstad et al . / The level structure "

n

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!. Rek.stad et al . ( The lenel .structure

37 7

5 .2 . DISCUSSION OF THE POSITIVE-PARITY STATES

The model applied to the negative-parity states was based on a standard BCS approach for the pair correlations and with the full Coriolis coupling strength 2). It is well known that this model does not fit the Coriolis perturbed i,3î2 bands observed in odd-neutron nuclei throughout the whole rare-earth region without introducing an ad hoc reduction of the Coriolis coupling strength 4). It has recently been demonstrated a) that this attenuation problem possibly could solved by the inclusion of the two-body component of the recoil interaction in addition to the pairing force and by performing a diagonalization instead of using the BCS approximation. In the present analysis of the positive-parity band in 53Gd we apply the pairing-plus-recoil model (PPR) developed in refs. 3. 4). T'he hamiltonian takes the form where HB . P . describes the single-particle field (Nilsson type), HP . ;~ is the pairing interaction with the strength parameter G and H*o,o~ is the rotor hamiltonian given by Hrutor = (~ 2/2~) ~ (Ik-Jk)2 k=1.2

_ (h2/2~)(I2-I3)+(h2/2~X J2- .%3)-(h2/~)(I, J1 +J2.%2).

Both the rotor and the Coriolis term [first and third term on the r.h.s. of eq . (2)] are treated conventionally, while we for the recoil term within the language of second quantization use the following expression 3) (h2/~11,2-J3) _ (h2~~1~ ~ JV +1 ) - ~2lujnaJn +( ~, Sla~nClin)2 li. n i. n +

~

Jn.1~n~

b(1, ~)b(1~,

-~~n+~ajn~-i ai~n~ain(

with b(j, Sl) _ {(j-~l)(j+Sl+ 1)}~ . The pairing and the recoil tenu are diagonalized within a basis which consists of all possible states of the type

where {a} characterizes the set of occupied orbitals . The single-particle Nilsson basis includes orbitals of both types of parity . For computational reasons the basis was limited to the eleven Nilsson orbitals given in table 3. From a BCS analysis we know that the Fermi level should be between the + (660) and ~+ (651) levels . This means that our basic intrinsic wave functions contain four pairs plus one odd neutron.

J . Rek.stad et al . / The level structure

37 8

TAHI .f :

3

The single-particle orbitals used in the calculations on the positive-parity states in 's'Gd Orbit t (Nilsson notation)

Energy ** (keV)

~ - (514) u -(505)

0 818 1100 1339 1508 1762 2773 3128 3449 3741 4679

z'(660) ¢ - (530) ~ - (532) ~ + (651) ~ + (642) (521) i - (523) ç - (521) - (512)

Expansion coefficients j=i

-0 .073 0 .646

l=i

-0.053 0 .233 0 .298 -0 .025 0 .094

-0 .454

0 .386

.l=z

0 .195 -0 .495 0 .371 0 .107 0.040 -0 .329 0 .199 0.187 -0 .182

1= :

0 .044 -0 .513 -0 .717 0 .052 0 .038 -0 .056 -0 .882 0 .501 -0 .408

j=z

j =t.:'

-0 .037

0 .003 1 .000 -0 .035 -0 .214 -0 .337 -0 .069 - 0 .082 -0 .091 -0 .225 0 .134 -0 .001

-0 .404 0 .609 -0 .381 0 .336 - 0 .245 0 .787 -0 .362 0 .583 0 .894

j =t ~

0.885 0.930 0 .964

Energies and wave functions arc obtained from a Nilsson calculations with the same harmonic oscillator potential parameters used in ref. z), and with deformation parameters r.~ = 0 .19, i:, _ -0 .04 . The dN = 2 coupling has been neglected . * The inclusion of higher-lying orbitals originated from the i,~-a state gives minor effects only on the results for the positive-parity band. ** The single-particle energy has been normalized to the energy of the ; - (514) orbital .

The energy spectrum is calculated in the following way : one particle is fixed in a specific orbital while the other four pairs are distributed on the available orbitals to obtain the minimum for the intrinsic energy . The calculation is repeated with the unpaired particle placed in different orbitals, and in this way a complete set of band heads is generated. Finally we perform a standard Coriolis calculation within this set of intrinsic states . The following parameters are used in the calculation. For the rotational parameter ~i/2~ we take 16 keV. The pairing strength parameter is chosen to be Gp = 326 keV . This reproduces the odd-even mass difference as calculated from the two neighbouring even nuclei . Furter details of the model are given in ref. 2H). The results of the calculations on the positive-parity states are shown in fig. 7 together with the experimental level scheme. One should emphasize that in these calculations there is no ad hoc attenuation of the Coriolis matrix elements. For comparison we also show the analogous result obtained with the standard approach or the particle-rotor model with the recoil term included and where the pairing effect is described by means of the BCS approximation. Otherwise the same singleparticle potential and identical parameter values are used in the two calculations . The different results are caused not only by a reduction in the off-diagonal Coriolis matrix elements, but also by a difference in the intrinsic energies calculated by the BCS approximation or the PPR model, as shown in table 4. In the case of ts 3 Gd the main contribution comes from an increased separation of the intrinsic ~2 = and ~+ states.

J. Rekstad et al. / The level .structure E(MeV)

EXPERIMENT

MODEL BCS

379

PPR 25/2

25/2 19/2

19/2 25/2

0 .5

19/2

v2

z1n 312 7/2 5/2

0

n/z

zvz 1sn

15/2

1/2

1/2 17/2

~ 17/2

51~- 13/2 9/2

13/2 9/2

1sn

5/2

3/2 7/2

17/2

13/2 9/2

Fig . 7 . The results from calculations with the particle-rotor model are compared with the observed i, a,z band structure in '°'Gd . On the l .h .s . is shown the result when the two-body part of the recoil term is neglected and pairing is treated within the framework of the BCS approximation. The other calculation, labelled PPR, includes the two-body recoil effect and pairing is calculated by diagonalization. The need for an extra Coriolis attenuation is removed in the last case .

6. Summary

The present study of ts3Gd by means of the tsosm( a, n)tsaGd reaction has several interesting results, which are summarized below. The (a, n) reaction does not appear to behave like a normal compound reaction . The low y-multiplicities in tsaGd compared to multiplicities in tszCrd obtained in the same experiment give evidence for low-lying entry states corresponding to neutron energies in the range 6-7 MeV for the emitted neutrons in the (a, n) process. Further investigations of this phenomenon are in progress . TABLE 4

Some properties of the intrinsic states in the BCS and the PPR calculations Orbit (Nilsson notation)

}+(660) ~+(651) }+(642)

BCS

PPR

Eqp (keV)

att. factor 1

Eqp (keV)

att. factor 1

266 0 247

0.97 0.92

238 0 767

0.91 0.94

' The attenuation factor is defined as ( U, UZ + V, VZ) in the BCS calculation, while it is taken as the overlap between the two complete states in the PPR model .

380

J. Rekstud et ul. / 77te legel .structure

A number of new levels in 's3Gd have been found. The obtained band structure is very similar to the known structure of the 's' Sm nucleus, and it is in good agreement with a recent particle-rotor model calculation of negative-parity states in odd-mass N = 89 nuclei . The decoupled i } rotational band in ' s3Gd, as well as in other rare-earth nuclei, cannot be accounted for by the particle-rotor model in the standard approach unless the Coriolis coupling matrix elements are considerably reduced. The present calculation with the pairing-plus-recoil model (PPR) shows that this problem is removed if the two-body part of the recoil term is included, and the pairing interaction is computed by exact diagonalization instead of applying the BCS approxition. Financial support from the Nordic Committee for Cooperation based on Accelerators is acknowledged . References 1) J. Rekstad, E. Osnes and G. L$vh$iden, Phys . Lett . 62B (1976) 15 M. Guttormsen, E. Osnes, J. Rekstad, G. L$vh$iden and O. Straume, Nucl . Phys . A298 (1978) 122 T . Engeland and J. Rekstad, Phys . Lett . 89B (1979) 8 l. Rekstad and T. Engeland, Phys . Lett . 89B (1980) 316 R. G. H. Robertson, S. H. Choh, R. G. Summers-Gill and C. V. Stager, Can. J. Phys . 49 (1971) 2227 D. E. Nelson, D. G. Burke, W. B. Cook and J. C. Waddington, Can. J. Phys . 49 (1971) 3166 D. E. Nelson, D. G. Burke, l. C. Waddington and W. B. Cook, Can. J. Phys . 51 (1973) 2000 W . B. Cook, J. C. Waddington, D. G. Burke and D. E. Nelson, Can. J. Phys . 51 (1973) 1978 W . B. Cook and J. C. Waddington, Can. J. Phys. 51 (1973) 2612 10) B. Singh and M. W. Johns, Can. J. Phys. 52 (1974) 1160 11) O. Straume, D. G. Burke and J. C. Waddington, Can. J. Phys . 52 (1974) 1648 12) D. D. Warner, W. D. Hamilton, R. A. Fox and T. Al-Janabi, J. of Phys . G2 (1975) 230 13) W. B. Cook, M. W. Johns, G. L$vh$iden and J. C. Waddington, Nucl . Phys. A259 (1976) 461 14) G. Vandenput, L. Jacobs, J. M. van den Cruyce, P. H. M. van Assche, H. Baader, D. Breitig, H. R. Koch, K. Schreckenbach and T. von Egidy, Neutron capture information meeting and workshop, Grenoble, 1975 ; ILL report 75A186, 1975 15) D. D. Warner, W. D. Hamilton, R. A . Fox, M. Finger, J. Konicek, V. N. Pavlov and V. M. TsupkoSitnikov, J. of Phys. G4 (1978) 1887 16) P . O. Tj$m and B. Elbek, Mat. Fys. Medd . Dan. Vid. Selsk. 36 (1967) No . 8 17) H. L. Nielsen and K. Wilsky, Nucl . Phys . A115 (1968) 377 18) J. Borggreen and G. Sletten, Nucl . Phys . A143 (1970) 255 19) I . Rezauka, F. M. Bernthal, J . O. Rasmussen, R. Stokstad, I. Freest, J, Greenberg, D. A. Bromley, Nucl . Phys. A179 (1972) 51 20) G. L$vh$iden, S. A. Hjorth, H. Ryde and L. Harms-Ringdal, Nucl. Phys . A181 (1972) 589 21) G. L$vh$iden, D. G. Burke, J. C. Waddington, Can. J. Phys . 51 (1973) 1369 22) G. L$vh$iden and D. G. Burke, Can. J. Phys. 51 (1973) 2354 23) T. Tuurnala, A. Süvola, P. Jetai and T. Liljavista, Z. Phys . 266 (1974) 103 24) T. Tuumala, Z. Phys . 268 (1974) 371 25) S. A. Hjorth and W. Klamra, USIP Report 74-21, Sept . 1974 26) O . Streams, D. G. Burke and J. C. Waddington, Can. J. Phys . 52 (1974) 1648 27) G. B. Hagemann, R. Broda, B. Herskind, M. Ishihara, S. Ogaza and H. Ryde, Nucl . Phys. A245 2) 3) 4) 5) 6) 7) 8) 9)

(1975) 166 28) T . Engeland, Phys . Scripte, to be published