INTERMEDIATE STRUCTURES IN FISSION - SPECTROSCOPY OF SHAPE ISOMERS

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INTERMEDIATE STRUCTURES IN FISSION - SPECTROSCOPY OF SHAPE ISOMERS

S. Bjørnholm

To cite this version:

S. Bjørnholm. INTERMEDIATE STRUCTURES IN FISSION - SPECTROSCOPY OF SHAPE ISO- MERS. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-33-C5-44. �10.1051/jphyscol:1972504�.

�jpa-00215106�

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JOURNAL DE PHYSIQUE Colloque C 5 , supplement au no 8-9, Tome 33, ofi it-Septembre 1972, page C 5 3 3

INTERMEDIATE STRUCTURES IN FISSION -

SPECTROSCOPY OF SHAPE ISOMERS

S. BJ0RNHOLM

The Niels Bohr Institute, University of Copenhagen - ^Denmark

Rfsumf - ^Laspectroscopie des Btats de rotation et des Btats intrinsAques bgtis sur les isomers de forme qui se ddsexcitent par fission spontande est revue H la lumigre des donnees exp8rimentaAes existantes. Pour les noyaux pairs-pairs nous discutons la bande de rotation de l1$tat fondamental", les isomers d6s A la r&gle de selection K , l'excitation des vibrations et les &tats du noyau compose. Pour les noyaux ayant un nombre impair de neutrons nous discutons les excitations du neutron impair et nous les comparons au diagramme de Nilsson aux grandes d8fomtions ( c = 0.6).

Abstract - The spectroscopy of rotational and intrinsic states built on the spontaneously fissioning shape isomers is reviewed on the basis of available experiments. For doubly even nuclei, the "ground" state rotational band, K-isomers, vibrational excitations and compound levels are discussed. For odd-neutron nuclei the single-neutron excitations are discussed and compared to the Nilsson diagram at large distortions (E = 0.6).

I - INTRODUCTION

This paper is a summary of what we know about the spectroscopy of the shape isomers in the uranium region.

For many years we have thought that if you want to induce fission in a heavy nucleus, you have to pull it out. The surface tension which may include shell effects resists this, but Coulomb repulsion helps. When you pass a critical elongation, the saddle, the nucleus spontaneously flies apart in two pieces. Many nuclei behave that way. However, starting with the pio- neering work of today's chairman and his co- workers, we have learned that some nuclei, from thorium to berkelium, will resist as usual when you pull them, they will reach a critical elongation, but then they will go - ^snap- into a new quasistable configuration with a ratio of axes of about 1:2, and you have to pull once more to induce fission. This second shape is not all that stable but apart from that, it is as good a nucleus as any ground state we know of. In a sense it is a better nucleus. This is illustrated in

.

¹RATIO OF AXES ²

FIG.l - ^Thespontaneously-fissioning shape isomers have higher symmetry than ordinary non-spherical nuclei. This should be reflected in their excitation sDectra.

figure I: Since the days of antiquity it has generally been agreed that the sphere, which has the highest symmetry, is the most beautiful shape.

If the neutron and proton numbers are right,

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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972504

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shell effects associated with the symmetry, will ensure that the nucleus takes the most beautiful form, the sphere. Conversely, if the nucleon numbers are wrong, the same shell effects will force the nucleus to avoid the sphere and assume a wrong ground state shape with lower symmetry.

The shape isomers occur in nuclei with nucleon numbers wrong with respect to the sphere. They have found a shape with a symmetry - a ratio of axes of 1:2 - for which their nucleon numbers are right. In this sense they are more beautiful than the ordinary non-spherical ground states.

The following is a status report of the spectroscopy of this isomeric shape. It is still in an embryonic stage, but it may be expected that this spectroscopy will become something more than a trivial extension of what has been learned al- ready from the spectra of ordinary deformed nuclei.

The higher symmetry - the "magic" ratio of axes -

should influence the spectra and lead to novel features which it will be of special interest to explore.

I1 - SPECTROSCOPY OF DOUBLY EVEN SHAPE ISOMERS Plutonium 240 is the best studied case.

In a measurement, which I will not hesitate to call the experiment of the year, Specht, Konecny, Heunemann and Weber have identified the E2 conversion lines of the ground state rotational band, built on the shape isomeric state. The isomer is formed in the 238~(a,2n) reaction and the traditional technique of measuring the low lying transitions, forming the "heavy traffic line" to- wards the ground.state, is used. Figure 2 illustrates the situation. Below, the fraction of the total cross section that goes through various chan- nels is given. In a typical example, 172~b,it is 90 per cent. For the 240~u isomer it is per cent, so the traffic is not really heavy at all.

How the Munich group solved this difficulty is described in ref. [l]. Their result is given in figure 3. The band has a moment of inertia more than twice larger than the corresponding band in the first well and the energy spacings are extremely close to the adiabatic, I(I+l), limit.

Figure 4 illustrates another important spectroscopic measurement, due to Limkilde and Sletten [2]. In the first well of 238pU, a, in

"HEAVY " TRAFFIC LINES

k

n Fission

/~!!j

If:'

^o+²⁺ Deformation

L

FIC.2 - Flow diagram for the deexcitation of a fissile compound nucleus with two competing wells.

The last part of the deexcitation cascades will consist of y-rays and conversion electrons. The low level density near the ground state ensures relatively heavy population of the low lying states.

Heunemonn, Konecny Specht and Weber

KeV

SECOND WELL

A D = 3 . 3 KeV ( AI 57.1 KeV)

FIG.3 - The rotarional band built on the 4 ns s ontaneously fissioning shape isomer of "OPU, ref. [I].

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SLETTEN AND LlMKlLDE

K- Isomer ,,,

W 2 A

41 - 0 5 n s * S F

OO+J Deformation ^*

I

FIRST SECOND

WELL WELL

FIG.4 - Isomerism due to the K-selection rule is a well established phenomenon in non-spherical nuclei (first well). Such isomers should also -

and are indeed - found in the second well. (The K , I ~ = 4.4 isomer in the first well 2 3 8was ~ ~

identified by Bengtson et al. [3] .)

( NEUTRON ) ENERGY GAe 2A,

FIRST WELL SECOND WELL

FIG.5 - Summary of two-quasiparticle isomers

many other doubly even nuclei, there exists an isomeric state which is generated by breaking a neutron pair and coupling the two spin projec-

tions to a large K-value which hinders the y- decay to the ground state levels. The excitation energy is that required for breaking a pair. It meashres the magnitude of the neutron energy gap

2A with a determinacy of about 0.2 MeV. In 2 3 8 ~ u there are also two fission isomers. Al- though the U-values remain unknown, the authors of ref. [2] have successfully measured the energy difference to be 1.3i0.3 MeV. Figure 5 compares their result to the situation in the first well for various K-isomers of doubly even nuclides in the vicinity of 238~u. The figure also shows the odd-even mass difference Pn derived from the neutron separation energies, another experimental measure of che neutron energy gap. (The proton gap is nearly always larger.)

By ingenious extension of traditional techniques, we thus know the ground state rotational band and the (neutron) energy gap for the shape isomer. The specific nature of the isomeric state, enclosed as it is between two relatively low barriers, provides a unique possibili- ty of measuring the spectrum of vibrational states at higher energies - in the energy interval from about one to zero MeV below the barrier top. The state must be predominantly of the 6-vibrational type, i.e. of the stretching type that leads to fission. Figure 6 shows a text- book version of a double humped barrier [7]. It is symmetric and only one degree-of-freedom is considered. The well between the barriers holds a number of quasibound states. They can decay by tunneLLlng through the barrier and hence have finite widths which increase as the barrier top is approached. Waves coming from the left will penetrate the double barrier, and if the energy of the incoming wave matches the energy of the bound state, the penetrability will be unity, as shown to the right in figure 6. An asymmetric barrier, figure 7, which is more realistic, will

also give resonance transmission, but with peak transmissions lower than unity. As before, the energy width of the transmitted wave is equal to the width of the quasibound state and hence to the inverse lifetime. Compound motion in the first well (not shown) simulates a broad-band spectrum of incoming waves. If the compound levels in the first well are populated uniformly, by a (d,p) process for example, one will observe an enhanced fission probability at the resonance

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F1G.7

-

The same as in figure 6, except now the two barriers differ in height and width, ref. [7]

.

2.0 4.0 6.3

ENERGY (MeV)

FIG.6 - Left, a symmetric double-humped barrier showing quasibound states.

Right, the penetrability curve showing complete transmission at the position of the quasibound states. The two barriers act as a double layer mono- chromator, ref. [7] .

energies. Figure 8 shows such resonances in 240~u, ref. 181. They are rather broad. There- fore one would at first be inclined to say that the barriers defining the resonances must be quite thin. This actually is not so. There exists a measurement [9] of the 4.9 MeV resonance made with higher resolution, figure 9. What appears

to be a broad Lorentzian shape has indeed fine structure with energy spacings comparable to the total level spacings expected in the second well at this excitation energy: 2.9 MeV. So, we are reminded of the oversimplification introduced when treating the problem in one degree-of-freedom only. It is no real surprise that the B-vibra-

tional motion couples to other degrees-of-freedom and leads to configuration mixing. The measurement, figure 9, shows how much mixing there is,

and that is a piece of information which it has never been possible to extract from measurements of vibrations of the ordinary shapes, belonging to the first well. In fact, two-phonon or higher vibrational states of deformed nuclei have not yet been identified in ordinary deformed nuclei.

The specific property of the stretching vibrations in the second well, namely that they and only they lead to fission, makes it possible to study them separately. In addition, a measurement of the fragment angular distributions should in principle lead to the determination of the quantum numbers, I,K of the vibrational states. n In practice this has only been possible to a limited degree. Here, Y-ray induced fission with monochromatic Y-rays has the advantage of picking out the 1- and perhaps 2+ resonances exclusively.

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SHAPE ISOhlERS

. , ,

3.0 L.0 5 0 6.0 7.0 8 0 EXCITATION ENERGV (MeV)

FIG.8 - Resonance barrier penetration in 2'0~~.

Compound levels in the first well are populated in the (d,p) process after which fission takes place in competition with y-emission. The

total proton spectrum is shown above, the fraction of protons followed by fission is the lowest curve, ref. [ B ]

.

EXCITATION ENERGY IN 2 4 0 ~ v (McVI

FIG.9 - Sigh resolution ineasurement of the 4.9 MeV resonance shown in figure 8, ref. [ 9 ] .

There is some interesting recent work by Knowles along this line [lo].

At still higher energies the coupling of the fission motion to other degrees-of-freedom is expected to wash out the vibrational resonance structure completely. This is equivalent to compound nucleus motion. In the neutron induced fission of 2 3 9 ~ ~ with resonance neutrons, one observes intermediate structure in the fission probability of the l* capture states [11,12].

The spacing, 0.46 keV, reflects the level density

of the 1' compound states in the second well.

Figure 10 summarizes the spectroscopic information obtained so far for a typical doubly even shape isomer, 240~u. (The K-isomer actually belongs to 238~u, but this is no serious distortion of facts.) Compared to the wealth of spectroscopic information existing on the excitations of the ordinary ground state shape, the results are modest.

But it is a beginning. With respect to the higher lying vibrations, the picture is actually quite advanced, as stressed above.

We conclude this section on doubly even nuclei with a comparison of experiment and a recent theoretical calculation due to A.

Sobiczewski [13], figure 11.

MeV

L.53 1' compound states

-

D, =.L6 KeV

1.3 t0.3 111 = ? K - isomer

:" ;

^0.8'

.069

\

^0.6'0.4; ^{Gr s t}rotational ,022

,000 ^0.2 band

- o.o+

2 b o m P u . E n w 2.0 MeV

' -

SECOND WELL

FIG.10 - Summary of the available information on the level structure of a doubly even shape isomer,

2 ' 0 ~ ~ (and 23e~u), refs. [1,2,8,9,11,12].

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the pairing strength.

DEFORMATION, E

NEUTRON ENEUGY GAP IN 238,Z'0 PU

f

1

First Wetl / ^S ^e ^c ^Z ^l

Experiment

FIG.ll - Comparison of experimental and theoretical values of mqment of inertia of the completely paired, 0 , configurations (top) and of the neutron energy gap for different deformations (below), The theoretical results [13] are based on the Nilsson model. (No experimental value of 2Pn is given for the second well. There exist experimental mass values for the plutonium shape isomers, but there is a problem of consistency with the corresponding data for the americium

isotopes.)

Above, the experimental moments of inertia are compared to a cranking calculation, including pairing. The deformation E of the isomer is assumed equal to 0.6 on theoretical grounds.

That is where the second minimum lies according to the Strutinsky type calculations [14,15,16]

.

It corresponds to a ratio of axes of 1:2. The agreement is good, but it is not possible to say whether a pairing strength proportional to the surface area, G % S, should be preferred over a constant pairing strength, G ^%const. Below, on figure 11, the calculated neutron energy gap in the two versions, G 'L S and G 'L const., is compared to the experimental values of the

(neutron) energy gap. (Once more, a possible difference between 238~u and 240~u is assumed to be negligible.) The agreement is satisfactory, but uncertainties are again too large to allow for a definite choice between the two versions of

A comparison of the experimental quadrupole moment - including its sign - and hence of the deformation of the shape isomer with the theoretical value would have been most interesting. This regrettably has to await further progress in experimental techniques.

I11 - SPECTROSCOPY OF ODD-A SHAPE ISOMERS The odd-A nuclei can be thought of as a doubly even core to which an extra particle is coupled. With the core in its ground state the odd particle determines the spin, Q-value and parity of the system as a whole. Different single-particle configurations, each with a given 62 n value, carry a different energy which may vary a good deal with deformation. This is the spe- cialization energy. It means that the double- humped barrier may look different for different single-particle configurations, In particular, the location and width of the fission resonances will vary with the value of nn. There will be a specific pattern of fragment angular distributions associated with each band of a given St n value. In principle one just has to find the fission resonance peaks, measure the angular distribution across the peak, and deduce Q , I ~ . Then one has to decide whether the resonance corresponds to the zero-order 6-vibrational motion of the core or to a higher order phonon coupled to the single particle. If it is the zero-order phonon, the resonance represents the single particle state in the second well with its associated rotational band.

In practice this is not so simple, but let us see how far the exploration of single- neutron states in the second well has advanced.

It will be wise to seek guidance from the carto- graphic works of the theorists. Figure 12 is one such map, due to Nilsson et al. 1141. The position of the second minimum is calculated from this map and found to be & = 0.60. The intersection of a vertical line at E = 0.60 gives the ordering of single-particle eigenvalues, shown in figure 13. The Fermi Level for a shape isomer with given neutron number is determined

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SHAPE ISOMERS C5-39

isomer-ratio analysis of the results they conclude that the four spin pairs shown in Table I are the most probable candidates for the two isomers, with the two additional ones being possible also, but less probable. The main as- sumption required is that the spontaneous- fission cross-section ratio is representative of the total isomer cross sections. If one isomer had a decay branch back to the first well, and the other did not, the conclusions would be wrong, but this seems unlikely. Taking guidance from the Nilsson diagram, figures 12 and 13, the authors of ref. [18] reject four of the six options, being left with the [505]11/2- as the

FIG.12 - Nilsson diagram for neutrons at large deformations [14]. Several other versions have been suggested, depending on the choice of the hexadecapole distortion parameter ~ 4 , and on the radial dependence of the otential: Harmonic oscillator, Woods-Saxon $51 or a folded Yukawa potential D6]. There are significant diffe- rences between the various versions. The above example is not unique.

by counting up from the bottom. It is denoted by F (for Fermi). For the two cases 2 3 7 ~ u and 233~h both with N = 143, it is the Nilsson level

[N~,A]Q' = [862] 5 / 2 + . Similarly the Fermi level for 2 3 1 ~ h is the [512]3/2- configuration. Note the gap at H = 144 and the high-spin [505]11/2- state, F-3, which is responsible for a number of isomeric states in the first well at the beginning of the region of deformed rare earth nuclei

C171

In 2 3 7 ~ ~ there are two fission isomers.

One with a 1.1 ps halflife, the other decaying with a 0.08 us period. Russo et al. [183 have studied the relative population of these two isomers in compound nucleus reactions with different amounts of angular momentum brought into the compound system. They find that increased angular momentum favors the population of the 1.1 us isomer. Using the traditional, statistical,

[510 1 (IF, ^,;^{! ,}

,-

^{F - 2}

[ 5 0 5 ] 1 1 / F m F- 3 1752 1 3 1 ~

0

^{F - L}

z 0

-

[ 5 1 L ] 72- F - 5

Ln

2-t

1-

L

NEUTRONS IN SECOND WELL

FIG.13 - The order of filling of neutrons in the potential, figure 12, for E

-

0.60. Asymptotic quantum numbers are given on the left hand side.

The Fermi level, F, corresponding to two nuclei that have been experimentally studied, is indi- cated on the right hand side (N = 143).

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TABLE I

Possible Spin Pairs fqr Double Shape Isomers of 2 3 7 ~ u Russo, Vandenbosch, Mehta, Tesmer and Wolf

candidate for the long lived isomer and the [862]5/2+ as the most likely assignment of the short lived state. This is indeed the Fermi level in 2 3 7 ~ u and the 1112- state is the F-3

From measured R-dependende of reaction yields

From result above plus Nilsson diagram Interpretation

level. Altogether a very consistent picture;

though of course, spectroscopists working with

(912,1112) (712,1112) (712,912) (512,1112) - {(5/2,9/2) (3/2,11/2)}

4 4

5/2+,11/2- {3/2-,1112-1

states in the first well may have to recall the 1.1 us: [505] 1112-

F-3

very early days of their trade to find such re-

0.08 us: [862]5/2+ {or [512] 312-1

F F-1

sults satisfying.

The barriers surrounding the isomers of 2 3 7 ~ u are 2-3 MeV high. That is why the life-

FIG.14 - The hitherto most conspicuous example of a fission resonance associated with an intermediate state in the double- humped fission potential. It is assigned as a R = 1 single-neutron state in the second well of 2 3 1 ~ h , ref.[l9].

times are microseconds. The widths that one should find in a resonance experiment designed to reveal these states are correspondingly of the order of eV, i.e. impossible to measure.

The situation is different with the thorium isotopes. Here, the second well apparently is very shallow so that the widths become measur- able, typically 10 keV or more. Figure 14 shows the result of Lynn, James and Earwaker [19] for fission induced in 2 3 0 ~ h by 600-1400 keV neutrons with an energy resolution of 5 keV. The fragment angular distributions in the region of the peak shows uniquely that the R-value is one half. The various rotational states of this R = 4 band are hidden in the peak. By extremely careful high-resolution measurements [19,20] of the fragment angular distributions at the flanks and across the top of the peak, the outline of a strongly decoupled rotational band emerges.

Nature has been unkind in this case. The angular distributions are not as rich in structure as one might justly have expected with a better behaved value of the decoupling parameter (a).

Figure 15 summarizes the most likely interpretation of the results for 231~h. In addition to the Q = 1- band which fits very naturally as the F-1, [510] 112- configuration at neutron number, N = 141, there is evidence of a 'R = 312- resonance, i.e. the Fermi level itself [512] 312- (see figures 12 and 13).

The uniqueness and in particular the

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SHAPE ISOMERS C5-41

h

% 2I

Y

I

LYNN. JAMES AND EARWAKER

A d W

ASSIGNMENT

W z SECOND WELL

W

FIG.15 - Single-neutron rotational band in the second well of 2 3 1 ~ h , ref. [19].

1.35 MeV neutron energy, i.e. in an interval of only 50 keV. The Moscow-Obninsk group has boldly applied a resonance analysis to the results and proposed two not very different versions to explain them: Five to six rotational bands in the second well with specific values of fin are responsible for the total fission cross section and the angular distributions. Figure 17 shows

purity of the asymptotic quantum numbers, as- FIG.16 - Fission fragment angular distributions for neutron induced fission of 2 3 2 ~ h between signed in this way, remains open to question. 0.95 MeV and 2.30 MeV of neutron energy [21]. In figure 12 one sees how states with the same

value of fill repel each other. This is equivalent to mixed asymptotic quantum numbers. In the vicinity of E = 0.6, the [510]1/2- and the

[750]1/2- states may be mixed, for example. As 10' a result the decoupling parameter is not well

determined theoretically.

The neutron induced fission of 2 3 2 ~ h is another case where the spectroscopy of fission resonances has been pushed quite far by Andro- a

senko et al. [21]. Here, the situation is in a

way the inverse of the 2 3 1 ~ h situation. There 1 0 12 1~

E. H36 ''

are no beautiful peaks in the fission excitation function like in figure 14, but the fragment angular distributions show very pronounced structure, figure 16. Note for example the dramatic change occurring between 1.30 MeV and

FIG.17 - Decomposition of the fission probability of 2 3 2 ~ h + n into resonance contributions with specific $pin projection quantum numbers and parity, fi , see Table I1 and ref. [21].

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TABLE I1

Possible Neutron States in Second Well from Fission Resonances and Fragment Angular Distributions in 2 3 2 ~ h + n

Androsenko et al.

their proposed decomposition of the measured fission probability curve. Each band is located at the lowest peak (or shoulder). In Table I 1 neutron energy is translated to excitation energy above the 233~h ground state (first well), and the Rs values proposed in the two versions are listed. The lowest band is quite near in energy to the 1/2- band in the neighbouring 2 3 1 ~ h , figure 15. One may now consult figures 12 or 13 to see if the experimental Rs values correspond to those predicted to lie near the Fermi surface of 233~h. Three out of five cases work well, particularly in case b; the remaining two do not.

It is easy to suggest these states to be due to octupole or quadrupole vibrations coupled to the pure single-particle states. The phonon energies are a bit low though, 0.2 - 0.25 MeV. In any case, this approach will be sure to explain everything and predict nothing. One could also take the works of other cartographers and see if their predictions are more amicable, see caption to figure 12. All in all, the study [21] of 2 3 3 ~ h represents a promising beginning and one can hope for further progress with this nucleus.

IV - CONCLUDING REMARKS

1

a

b

i

The spectroscopy of shape isomers is still in its infancy. Although the baby develops pro- misingly, it is premature to make status with

Energy (MeV)

Assignment Energy (MeV) Assignment

respect to those features of special symmetry which were discussed in the introduction. They

5.8 5.9 6.0 6.0 6.15

5/2+ 1/2+ 5/2- 3/2+ 3/2-

F F+2 ? ? F-1

--

5.8 5.9 6.0 6.05 6.15 (5.85)

512' 1/2- 512- 312' 312- (712-1

F F-2 ? ? F-1 (F-5)

are expected to reveal themselves in the level structure, for example through a relatively weak coupling between different degrees-of-freedom.

In conclusion, let us mention a few specific lines of attack where one can hope for progress in a not too distant future.

a. Doubly Even Nuclei.

1. A determination of the quadrupole moment of the shape isomer would be a spectacular con- tribution.

2. Rotational bands in isomers in addition to 2 4 0 ~ ~ could be studied.

3. There are several more candidates for K-isomerism, notably 2 3 6 ~ ~ , 2 4 2 ~ m and 244~m, where a determination of the energy gap could be attempted. The problem is that of finding the

o+, ground state fission isomer, which is likely to decay within picoseconds. Another interesting problem is to find out whether the K-isomers decay by gamma emission to ground in the second well or directly by spontaneous fission.

4. More precise determinations of the K,k TI

quantum numbers of the vibrational resonances would be useful.

b. Odd-A Nuclei.

5. The energy difference between the two isomers in 2 3 7 ~ ~ would be interesting to know.

It could lie anywhere between zero and several hundred keV.

6. There are presumably more double isomers

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SHAPE ISOMERS

besides the 2 3 7 ~ u case in the odd-N isotopes.

Similarly, the identification of double isomers in odd-Z nuclides would open the discussion of the theoretical proton level diagram.

7. The band structure associated with the 2 3 3 ~ h resonances could perhaps be studied more closely in order to confirm the assignments, derive moments of inertia, etc.

8. Application of perturbed fragment angular- correlation techniques may open the field of mag- netic moment measurements and perhaps also of quadrupole moments.

c. Doubly Odd Nuclei.

9. Vibrational type resonances have been found in 2 3 2 ~ a , [22]. So far, it has not been possible to assign quantum numbers.

10. Double fission isomers may also be found in doubly odd nuclei.

d. New Regions of Shape Isomers

11. A significant next step would be the dis- covery of a new island of shape isomers. The region around N = 118 and Z = 84 is the most promising candidate. Here, the shape isomers are expected to decay by y-emission 1231. This is a difficulty, but the cross sections could be higher than in the transuranium region, because compound nucleus fission is less likely to exhaust the reaction cross section.

References

[I] SPECHT (H. J .), KONECNY (E.) , HEUNEMANN (D.) [15] BRACK (M.), DAMGAARD (J.), PAUL1 (H.C.), and WEBER (J.), Proceedings of this conference JENSEN (A.S.), STRUTINSKY (V.M.) and WONG 1972, vo1.2, communication 1.6. (C.Y.), Rev.Mod.Phys., 1972, to appear.

[2] LIMKILDE, (P.) and SLETTEN (G.), ibid., 1161 BOLSTERLI (M.), FISET (E.O.), NIX (J.R.) and vo1.2, communication 1.5. NORTON (J.L.), Phys.Rev.C, 1972, 5, 1050.

[3] BENGTSON (B.), JENSEN (J.), MOSZYNSKI (M.) and [17] BORGGREEN (J.) and SLETTEN (G.), Nucl.Phys., NIELSEN (H.L.), Nucl.Phys.,l970, A159, 249. 1970, A143, 255.

[4] BJsRNHOLM (S.), BORGGREEN (J.), DAVIES (D.) , [18] RUSSO (P.A.), VANDENBOSCH (R.), MEHTA (M.), HANSEN (N.J.S.), PEDERSEN (J.) and NIELSEN TESMER (J.R.) and WOLF (K.L.), Phys.Rev.C,

(H.L.), Nucl.Phys.,l968, A118, 261. 1971, 3, 1595.

[5]BRINCKMANN(H.F.),CLARK(D.),HANSEN(N.J.S.) [19]LYNN(J.E.),JAMES(G.D.)andEARWAKER(L.G.) and PEDERSEN (J.), to be published. Nucl.Phys., 1972, to appear.

[6] HANSEN (P.G.), WILSKY (K.), BABA (C.V.K.) and [ZO] YUEN (G.), RIZZO (G.T.), BEHKAMI (A.N.) and VANDENBOSCH (R.S .E. ) , Nucl .Phys., 1963, 45,410. HUIZENGA (J.H.), Am.Phys.Soc.Bull.II, 1971, [7] CRAMER (J.D.) and NIX (J.R.) , ^Phys^.Rev.C, 6 , 56, and private communication to the

1970, 2, 1048. authors of ref. 1191

.

[8] BAK (B. B. ) , BONDORE (J . ^P.⁾^,OTROSCHENKO (G.A. ) [21] ANDROSENKO (C .D. ) , ERMAGAMBETOV (S . ^B.^1.

PEDERSEN (J.) and RASMUSSEN (B.), Nucl.Phys., IGNATJUK (A.V.), RABOTNOV (N.S.), SMIRENKIN

1971, A165, 449. (G.N.), SOLDATOV (A.S.), USACHEV (L.N.),

191 SPECHT (H.J.), ERASER (J.S.), MILTON (J.C.D.) SPAK (D.L.), KAPITZA (S.P.), TSIPENJUK (J.M.) and DAVIES (W.G.), Physics and Chemistry of and KOVACH (I.), Physics and Chemistry of Fission, LAEA, Vienna, 1969, p.363. Fission, IAEA, Vienna, 1969, p.419.

[lo] KHAN (A.M.) and KNOWLES (J.W.), Nucl.Phys., [22] MUIR (D.W.) and VEESER (L.R.), Proc. of 3rd

1972, A179, 333. Conf. on Neutron Cross Sections and Techno-

[ll] WEIGMANN (H.) and THEOBALD (J.P.), Proceedings logy. 1971.

of this conference, 1972, vo1.2, communication [23] BJORNHOLM (S.), BORGGREEN (J.) and HYDE

1.4. (E.K.), Nucl.Phys., 1970, A156, 561.

[12] WEIGMANN (H.) and THEOBALD (J.P.) , Nucl .Phys., 1972, A187, 305.

[13] SOBICZEWSKI (A.) and BJORNHOLM (S.) , to be published.

[14] NILSSON (S.G.) , TSANG (C.F .) , SOBICZEWSKI (A.) ,

SZYMANSKI (Z

.

⁾^,WYCECH (S. ) , GUSTAFSON (C. ) ,

LAMM (I.L.). MOLLER (P.) and NILSSON (B.), Nucl.Phys., 1969, A131, 1.

(13)

DISCUSSION

H. NIFENECKER ( S a c l a y ) S . BJBRNHOLM ( ~ i e l s Bohr I n s t . )

HOTN can you e x p l a i n t h a t t h e l i f e times of t h e I t h i n k t h e shape isomers a r e t h e r e , but t h e y e x c i t e d s t a t e s i n t h e second well a r e l o n g e r decay by p e n e t r a t i o n of t h e i n n e r b a r r i e r and t h a n t h e ground s t a t e l i f e time ? emission of gamma r a y s .

S . BJBRNHOLM ( N i e l s Bohr I n s t . )

The e x c i t e d s t a t e h a s a higher energy because energy i s r e q u i r e d t o break a p a i r and form a t w o - q u a s i p a r t i c l e c o n f i g u r a t i o n w i t h d e f i n i - t e quantum numbers K ~ T h i s i s t r u e f o r a l l . shapes, s o t h e e f f e c t i v e b a r r i e r seen by t h e e x c i t e d s t a t e i s a s high a s t h e one seen by t h e ground s t a t e . B e s i d e s , t h e i n e r t i a a s s o - c i a t e d with t h e b d r i e r p e n e t r a t i o n i s l i k e l y t o be h i g h e r f o r an unpaired system t h a n f o r a completely p a i r e d system. T h i s would make t h e l i f e time longer f o r t h e t w o - q u a s i p a r t i c l e s t a t e .

J. JASTRZEBSKI ( Pologne)

Can you comment about t h e non e x i s t e n c e of Np spontaneously f i s s i o n n i n g isomers ?

E. R . HILF (Darmstadt)

The t h e o r e t i c a l p r e d i c t i o n ( s e e CROOKE e t a l . Nucl. Phys. A129 (1969) 513) of t h e small is- l a n d of shape isomers n e a r Ra r e s u l t e d from t h e i n t e r p l a y between t h e s u r f a c e and c u r v a t u - r e t e n s i o n x i n t h e l i q u i d drop model which y i e l d s a f l a t a t t h e t o p o r even double humped b a r r i e r f o r n u c l e i n e a r Ra, t h e l i g h t e r (hea- v i e r ) ones having only one s a d d l e of c o n s t r i c - t e d ( e l l i p s o i d a l ) shape. Then R.W. HASSE (Ann.

Phys. 68 (1971) 377) c o u l d show t h a t t h i s e f - f e c t of t h e LDM i s not s p o i l e d by t h e addi- t i o n a l terms of t h e d r o p l e t model. I n t h a t a r e a a t l e a s t t h e D.M. f l a t t e n s t h e t o p of t h e bar- r i e r and t h u s a l l o w s f o r t h e s h e l l e f f e c t s dig:

ging a second w e l l d e s p i t e t h e s t e e p b a r r i e r , i f only x i s s u f f i c i e n t l y l a r g e , a t l e a s t t h e 9 MeV of V. GROOTE b a r r i e r f i t . However B.MYERS and W. J. SWIATECKI ( p r i v . Comm. a t t h i s Conf. ) now end up with x 0 MeV

.

Thus t h i s i s l a n d of shape isomers may not e x i s t .