Orbit flip magnetic transitions

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Publis Wng Co., Amsterda"s physics 38 (1962) 186-192 ; (g) North-U011and

written permission from the publisher t or microfilm without be re?, roduced by photoprin

FLIP MAGNETIC TRANSITIONS Department

of

H. MORINAGA and K. TAKAHASHI Physics, University of Tokyo, Bunkyo-ku, Tokyo, Japan Received 24 May 1962

deformed nuclei it sometimes happens that a magnetic transition between two the particle . Two M4 nuclear single particle (Nilsson) states depends only on the orbit flip of were investigated and 179 and one in YbIll, which correspond to such a case transitions, one in Hf respectively. Further survey than 500, 2000 and more wcre found to be inhibited by factors of strongly hindered. Proton transiwhich are of this type revealed three more neutron transitions seems selection rule to indicate hindered at all. This are not tions of this type on the contrary orbit inside a nucleus. the neutron associated with electric current clearly the absence of an

kwact : in well

1. Introduction For performing a shell model calculation to estimate the magnetic transition probabilities, one must know, besides the appropriate wave functions, the strength of the interaction which causes the transitions . The strength of the spin and orbit flip interactions f,-)r protons and neutrons in nuclei are usually assumed to be equal to the g yromagretic ratios for free particles; g,(p) = 5.7, g,(n) = -3.8, g j(p) = I and g,(n) = 0. But, as we know well, these assumptions are of a very approximate nature and actually, we have good reasons to suspect that the values of g., are substantially reduced '). Although the effective gyromagnetic ratios are vitally interesting to nuclear physics, it has been rather difficult to estimate them since either the wave functions or the experimental transition probabilities have not been known accurately enough . For example, even with the M4 transitions where the pertinent states are well defined and the experimental transition probabilities are well known, it was not possible to find out any systematic variation in the rate of proton and neutron transitions '). Since there always exist both contributions of the spin and orbit flip (except for the MI transition which is a pure spin flip) in a magnetic transition between single particle states in spherical nuclei, it has been difficult to separate the two contributions . Ti1is situation, however, does not occur in the case of well deformed nuclei . Between Qc OnNe particle Nilsson states ofa well deformed nucleus, it sometimes happens that t hi, contribution to the magnetic transition from the spin flip vanishes in the asymptotic limit of large deformation, leaving the orbit flip entirely responsible for the transi", :on . Thus, it should be possible here to observe the contribution of the orbit flip directly and estimate the values of g, for nucleons inside a nucleus . A large in186

T ~°L.~~

A~t~iF~`IC

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~ g7

in the neutron transitions, if r (n) is actually pro, that is, if the hibitian stay a neutron orbit d s not carry an electric current . n inhibition ofthis sort was point out by ottelson a,nd ilsson ~) as a possible explanation of the slowness of an unhindered transition in ~ s' lZecently, we found two transitions :which are inhibited y large factors, ap parently because of this effect . In this air our ex rirnental results will discus d together with other cases of the orbit flip magnetic transitions . 2. It seems to be most fruitful to investigate tt~e hay°ioa~r of transitions in well def®tined nuclei, since it has beEn observed as one of the successful features ofthe shell transitions behave quite unifo ly, showing ahaays their characmodel that the teristic reduced transition probability . So far, ho ~ever, there has been no case where n observed tween ¬he ~üsson states o the defo ed nuclei. an 11rI transition has The weal established -~-- [510] isomeric state of f'~~ at 3~S key decays to the 215-key ~ -- [514] state by a hindered 3 transition with a half life of 14 sec ~). The latter state decays further to the ground ~ ~ ~6~ ] state with a hindered 1 cross-over decay transition (f g . 1(a)). here, one might ex ct an unhindered hif

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~ig . 1 . De+cay s~hc~es of Hf"~°° (~) and l~bl®'~ (b) . Th~ ~nerg~ s ar~ gi~~n in

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directly to the ground state. Frorn the as~~~&~ totic uanturrt numbers of the involved states, this transition must demand on the c+rbit ip of a neutron . If the transition probability of this cross-over were equal to that given by the single particle estin~.ate, the intensity ofthis cross-over should amount to approxi ately sweral ~rcent of the cascade intensity . In order to detect the cross-over transition, `vc irradiated th etallic and o~i e -1 reactor at 3apan to is -~ nergy~ aware samples of a natural hafnium in the J Institute, and looked. for the 375-keV ganZnlla ray with a conventional ~ulticha ncl scintillation spectrometer with a 3.1~ x 3.8 cm aI{Tl) cr~rstal . For eli mating the su peak and also the unnecessarily strong 215-key radiation a 12 ~nr thick lea a sor r was inserted between the source and the crystal . Because o t e lar e reduction factors, from the isF~meric state

AND K. TAKANA H. MORINAGA

dangerous to use the calculated aib rption-by lower ener~'es, it was felt especially for to gamma My energies of thV spectrometer at various the absorber . Therefere, efficiencies (145 keV), known calibration source: were measured with a number of well (411 keV), Pb203 (279 keV and 400 keV), Crsi (325 keV), Au 11f-9M (215 keV), the efficiency curve obtained for the spectrometer. an ,-,ßa22 (511 keV) . Fig. 2 shows

W Z

ENERGY (keV)

Fig. 2. Counting efficiency curves of the scintillation spectrometer with a 12 tween the source and the detector.

mm lead absorber be-

Since both the shorter and longer activities produced in the hafnium sample bothered our measurement, the change ofthe spectrum with time was followed carefully. Fig. 3 shows a spectnim taken about 60 see after the irradiation . Here, the short lived activity is already gone and the contributions from the longer lived activities are already subtracted. The arrow shows the place where the 375-keV gamma ray should appear . The intensity of the 375-keV gamma ray was determined comparing its photopeak area to that of the 215-keV gamma ray. The branching ratio of the crossover thus found was about 5 x 10-3% of the cascade decay. This means that the cross-over M4 transition is inhibited by a factor of 2000 over the Moszkowski single particle estimate 5). An exactly parallel case of the cascade from the [510] state through the [514] state to the ground [624] state has been found in Ybr '7 '), which has the same number of neutrons as Hf 171 (fig. 1(b)). In this case we have failed to detect the corresponding

MAGNEnc

cross-over uansitiocr. The mit of this cross-over w Moszkowski single particle estimate.

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0.2

of the

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CHANNEL NUMBER

Fig. 3. Pulse hei t s

run of a hafnium sample irradiated by neutrons taken with a 12 mm lead between the sample and the detector. :t or

3.

t

p Neutron T

There are few other . where the magnetic transition depends or, the orbit flip. in ref. -). The two The case of an M2 transition in W'8' has n already discus 89 very similar M3 transitions in Os' and Os' 9 ' seem to fall in this category very nicely. They cur between 9y - [505] and - (5121 stag. Although they are in tht edge of the deformed region, there are many recent indications that the Nilsson's model applies quite well to these odd nuclei . Actually one observes very high hindrances for these transitions') one (Os' 89) being hindered by a factor of 5 x 1W and the other (Osl9 ') by a factor of 2 x 104. It is tempting to attribute this inhibition to the pure orbit flip of neutron since there has been no other satisfactory explanation for these transition rates. The case of Os'83, on the contrary, is more problematic . If the isomer pair is î9 #- [510]-9+ [624) as in the other N = 107 nuclei, H6 and Yb'77, and as it has been assigned 3-"), the transition should be an M4 orbit flip neutron transition . But in this case the experimental hindrance factor is only 12, indicating that the transition is

190

H . MORINAGA AND K. TAKAHAM

carefully ehecked and the decay of practically unhindered. The M4 character has been the [624] assignment . for the ground the Z + state to Re 183 is quite consistent with state 8) this seemingly natural assignThere are three arguments which cast doubt upon ment of [510] orbital to the isomeric state : (l.) The [510] - [624] energy difference in the neighbouring riucleides is known from the Nilsson in several cases and is always 350 to 400 keV. Also it is expected on the deformation . diagram that this energy difference depends very weakly 83 One should therefore expect the [510] orbital in Os' at about 350 to 400 keV above the [624] ground state. The observed energy of 170 keV is definitely too low. (2) Both experimentally and theoretically the energy of-the -- [5211 hole state is known to be shooting up rapidly with decreasing deformation i .e. with increasing mass number . The state already appears at 7415 keV below the [624] state at W18I 9) . It is, therefore, not strange at all to find the - [521 ] hole . state 170 keV above the [624] orbital in OS 183 (3) If the isomer were the [510] orbital one should expect a K capture decay to the [400] band which should appear slightly below 600 keV in Re' 83 . If, however, the isomer is the I - [521 ] state the decay to this state becomes first forbidden hindered . The failure to observe such decay 8) seems to support the latter assignment. Under the reassignment of the isomer to the I - [521 ] hole state, which is connected to the ground state by an unhindered spin flip M4 transition, the normal transition rate of the decay is also understood. A similar consideration of the energies of the states may be applied to classify the seven minute isomer of W179 . Here, the transition is an M3 and the 7-- [514] assignment for the ground state is unquestionable 3). The experimental hindrance factor of this M3 transition is 7 x 104. Either l ' - [510] and 1-- [521] states maybe successfully assigned to the isomer from consideration of this hindrance factor alone, since in the former case the transition is hindered because of the selection rule in the asymptotic quantum numbers and in the latter case because of the pure orbit flip of the neutron . The energy of the [510] state, however, should be more than 60()keV whereas the [5211 hole state should appear below 300 keV. The experimental energy, value of 222 keV leads us to prefer the [521 J assignment . This is then probably another case of hindrance due to the pure orbit flip of a neutron 4. Orbit Flip of a Proton It is interesting to see if there is any hindrance of magnetic transitions which depend only on the orbit flip of a proton . Two cases of this type are listed in the tabulation of the electromagnetic transition probabilities in ref. 3). One Ta 18 '

is an M3 transition in

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1FLJP MAGNMIC

191

where the measured hindrance t is 200 and the other is an M2 transition in Np"" where the hindrance is 70. In a further survey of the Nuclear Data Sheets ' °) two more M2 type orbit flip proton transitions were noticed. One is a 476-keV transition in Tale ', and the other is a 361-keV transition in Ho's5 . The values ofthe hindrance factors are 100 for both cases . Furthermore, according to the recent data in ref. 8), another M2 t orbit flip proton transition was found in Re' 83r A hindrance factor for this case. of 200 is obta 5. DÎsc"ons The orbit flip magnetic transitions so far identified are summarized in table 1 . It is clearly seen that all the neutron orbit flip transitions are inhibited by large factors . TABu 1 Summary of orbit flip magnetic transitions in deformed nuclei Nucleide

Orbital assignments

Classifica-

tion

Initial

__

Final

--

"; 70Yblst07

M4(n) M4(n)

Î-0101

11+16241

9,®8

M3(n)

[5121

- [5`151

71Hfi®â

lis

,40s8 8  e 94Wnmos ae1 t4WI os

et 7aTa lloo ,,NP 187 144

tee asRe,oa

i III 73Tatoe ies e 7 HQoe

k-[5101

M3(n)

M3(n) M2(n)

M3(p) M2(p) M2(p)

M2(p) M2(p)

[5051 j

-15211

+ [6241

2 x 10' >5x 108

11 ® [512]

5 x 104

-[5141

--13121

-~- [6241

(4111 - [5211 1, 1-(5141

I + [4041

}

°i-14021 11+0111

Hindrance

+ [6421 °+- [402)

® [5141 1 j - [5231

2 x 10' 7 x 104

7 x 10 8

2 ,x 10 8 7 x 10

2 x 1®8 1 x 102 1 x 101,

Theoretical hindrance factor

6®0.15

---® 6=0.23 6=0.26 X

2 x 108 2 x 108

102

6=0.30 3 x 108

3 x 108 6 Y 10

3 x 102

6 "~ 10 6 x 10

6 x 10

108

But there is only a small hindrance on proton orbit flip transitions . One must therefore be aware of this rather strong selection rule when discussing decay schemes of odd neutron nuclei in the deformed region . The effectiveness of the inhibition in the case of neutron transition, however, seems rather excessive considering that the quantum numbers describing the states are only asymptotic . Calculations of the transition probability with the Nilsson's wave function were therefore made to see how much inhibition is expected theoretically. The results are shown in the last columns in table 1 . Here, Nilsson's original wave functions 11 ) and the revised functions listed. i n ref. 3) were used and the values of gs and 91 for the neutron and proton were taken to be the same as their free values. For neutron transitions, the experimental hindrance factors are substantially higher than t B

on the later data listed in ref. '°).

192

H . MORINAGA AND K . TAKAHASHI'

for protod transithe calculated ones, by one or two orders of magnitudes, whereas well with the calculated values . tions the experimental hindrance factors agree quite protons is understood,, easily A moderate hindrance of orbit flip magnetic transition of systematic .differ, et of by the faci. that gI is considerably -smaller than g, The large experimental hindrance between proton and neutron, however, seems rather strange and suggestive in view of rather small difference in theoretical values . In any erase, it may be concluded that the effective current associated with the neu. tron orbit is much smaller than the current associated with the proton. This is contrary to the large effective charge of the neutron which usually amounts to the same order of magnitude as the proton charge . We are grateful to Dr . K. Kakihara for letting us perform this experiment at the JRR-1 Reactor of Japan Atomic Energy Research Institute . We should also like to thank Dr. T. Tamura for discussions . References 1) H. Miyazawa, Progr . Theoret . Phys. 6 (1951) 801 ; E. Kuroboshi and Y. Hara, Progr. Theoret. Phys. 20 (1958) 163 ; A de-Shalit, Proc. Intern . Conf. on Nuclear Structure, Kingston, Canada'' (North-Holland Publ. Co., Amsterdam, 1960) p. 90 2) M. Goldhaber and A. W. Sunyar, Chapter 16 of Beta- and Gamma-Ray Spectroscopy, ed . by K. Siegbahn (North-Holland Publishing Company, Amsterdam, 1955) 3) B . R. Mottelson and S. G. Nilsson, Mat. Fys . Skr. Dan. Vid. Selsk. l, No. 8 (1959) 4) Strominger, J. M. Hollander and G. T. Seaborg, Revs. Mod . Phys. 30 (1958) 585 S) S. Moszkowski, Chapter 13 of Beta- and Gamma-Ray Spectroscopy, ed. by K. Siegba.hn (:,%arthHolland Publishing Company, Amsterdam, 1955) 6) P. F. Fettweis, Proc. Intern. Conf. on Nuclear Structure, Kingston, Canada (North-Holland Publ . Co., Amsterdam, 1960) p. 606 7) J. O. Newton, Phys. Rev. 117 (1960) 1529 8) J. O. Newton, Phys. Rev . 11? (1960) 1520 9) B. Harmatz, T. H. Handley and J. W. Mihelich, Phys. Rev . 119 (1960) 1345 10) K. Way et cal., Nuclear Data Sheets (1960) 11) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk . 29, No. 16 (1955)