Atomic Energy of Canada Limited

MIRROR NUCLEI, A < 100

by

J.C. HARDY

Presented as an invited talk to the Canadian Association of Physicists meeting held in Montreal, June 18-21, 1973

Chalk River Nuclear Laboratories Chalk River, Ontario

August 1973

AECL-4604 Atomic Energy of Canada Limited

MIRROR NUCLEI, A <: 100

by

J.C. HARDY

Presented as an invited talk to the Canadian Association of Physicists meeting

held in Montreal, June 18-21, 1973.

Chalk River Nuclear Laboratories

Chalk River, Ontario

August 1973

AECL- Mirror Nuclei, A <, ICC

by

J.C Hardy

ABSTRACT

The effects of charge-dependent forces are described, and their dependence on the nuclear mass is discussed, it is proposed that large isospin impurities may occur in heavier nuclei (A 40 may be attributed to the proposed increase in charge dependent mixing. Some other experimental evidence suggesting the same conclusion is also given.

Chalk River Nuclear Laboratories Chalk River, Ontario

August 1973

*Presented as an invited talk to the Congress of the Canadian Association of Physicists held in Montreal, June 18-21, 1973. AECL-4604 Noyaux ~à miroir, A5 100*

J.C. Hardy

^Communication présentée, sur invitation, au Congres de l'Association Canadienne des Physiciens tenu a Montréal du 18 au 21 juin 1973. Résumé

On décrit les effets des forces dépendant de la charge ainsi que la mesure dans laquelle ils dépendent aussi de la masse nucléaire. On suggère que de grandes impuretés d'isospin sont susceptibles de se produire dans les noyaux lourds (A^ 100) oxi N ^ Z. Plusieurs catégories d'expériences a décroissance f3 sont sensibles à ces effets. On décrit en détail de récents travaux effectués a Chalk River pour étudier la décroissance supra-permise de noyaux 0 , !„ = -1. Ces travaux ont permis d'effectuer la première mesure des branches de décroissance Fermi "a miroir "à l'intérieur d'un multiplet T = 1. Ces données, ainsi que d'autres obtenues en ce qui concerne la décroissance $ suprapermise, sont analysées cotup te-tenu, particulièrement, des corrections dépendant de la charge auxquelles les comparaisons de miroir sont particulièrement sensibles. Les résultats obtenus sont commentés en fonction de la théorie des faibles interactions et de la question de l'existence d'un boson lourd de vecteur intermédiaire. On suggère que certains désaccords, pour les noyaux où k > 40 peuvent être attribués a l'augmentation proposée pour le mélange dépendant de la charge. Quelques preuves expérimentales, suggérant la même conclusion, sont également données.

L'Energie Atomique du Canada, Limitée Laboratoires Nucléaires de Chalk River Chalk River, Ontario Août 1973 AECL-4604 Mirror Nuclei, A <; 100

J.C. Hardy

In choosing the title for my talk, I had intended to attract those listeners who believe, as do most nuclear physicists, that for all practical purposes the study of mirror nuclei stops at mass 40. A description of some results with light nuclei, combined with a speculative discussion of the possibilities in extending such studies up to mass 100, seemed to provide the right balance between fact and fiction.

I now find that the CAP has taken matters into its own hands and advertised my talk as a description of mirror nuclei with

"A 2 100". Since it is problematic whether any nuclei fitting

that description are even stable, let alone accessible,

I am afraid that their great leap forward places me_ squarely

in the lunatic fringe. However, by retaining my original

intentions to discuss light, nucleon stable and reasonably

accessible nuclei, I hope to prove a certain degree of sanity.

If experienced the same forces regardless of

their charge, then mirror nuclei would be identical in every

respect. Simply changing the in a nucleus into

and vice versa would leave the nuclear energy levels,

transition strengths and so on unaffected. Furthermore, this

not only applies to levels in the mirror nuclei but to their

analogues in other nuclei with the same A as well. Under these

CAP - Canadian Association of Physicists conditions we should say that isobaric spin was a good quantum number since T commutes with a charge-independent nuclear

Hamiltonian.

In practice of course, the Hamiltonian is not charge independent, certainly the coulomb force plays a significant role in , and very likely charge dependence in the itself is also discernible. As a result, in crossing an isobaric multiplet between two mirror nuclei, one observes many differences, the most obvious being the large changes in ground-state energies. However, since the

Coulomb force is spin independent and has a long range it is not surprising that it affects the energies of states most strongly, and in a general sense the magnitude of the effect can easily be reproduced by calculations. A much smaller effect - and one that is more challenging theoretically - is

the change in the structure of the wave functions caused by charge dependent forces. To what extent does isospin remain

a good quantum number?

Superficially one might imagine that because the p Coulomb energy is proportional to z while the nuclear energy

varies more slowly with A, then charge dependent effects such

as isospin impurities would become more significant for heavier

nuclei. Actually, the total of all charge-dependent mixing

undoubtedly does increase for heavier nuclei but surprisingly

the same cannot be said of isospin impurities: it is well

known that analogue states are readily identified in all

nuclei up to the very heaviest. The explanation is not difficult to understand, and has particular relevance to mirror nuclei, so I shall spend a few minutes discussing it. Figure 1 shows schematically some of the effects of charge-dependent forces on the wave functions of a nucleus with Tz = §(N-z), a ground state isospin of T = | T | , and a variety of excited states with the same and higher isospin. The total effect on the ground state is seen at the top of the figure where all states, including those with the same T, are shown to mix with it. Obviously not all of this mixing contaminates the isospin of the ground state so actual isospin impurities must involve much fewer states, as represented by the diagram at the middle of the figure. Finally, the diagram at the bottom demonstrates an effect that is much more nearly accessible experimentally: the mixing of one specific T+l state with the ground state. Evidently this is the smallest effect of all. Two methods for detecting mixing with p-decay experi- ments are also displayed in the figure. The first illustrates that superallowed (Fermi) p-decay between analogue states, while insensitive to the total charge-dependent mixing, can provide a measure of the difference between such mixing in two members of a multiplet; this is possible, in principle at least, by comparing the measured transition intensity with calculations that assume perfect overlap between initial and final states. I shall return to this problem later. The second method requires measurement of the Fermi matrix element between two states that are not analogues of one another; in the example shown, this yields a value for the mixing between the initial state and the analogue of the final state. To get some idea of how these effects may vary from nucleus to nucleus in the periodic table, let us consider specifically the case of isospin mixing in the ground states of even-even nuclei. Most coulomb mixing will occur with excited states in which a has been promoted up one major oscillator shell1), if the ground state is represented by Pig. 2a then these particle-hole states are of the type shown in Pig. 2b and 2c. Since there is no -particle equivalent to Fig. 2b, these states have the same isospin T as the ground state, and cannot therefore cause isospin mixing; clearly the number of such states increases with neutron excess. Similarly only some of the states described by Fig. 2c have different isospin from the ground state, but the proportion of isospin-preserving states increases with the T off the nucleus. •Thus, although the total number of states involved in charge- dependent mixing increases for heavier nuclei, isospin impurities are actually quenched by the large neutron excess. The crucial conclusion must be that to study isospin-breaking effects one should look to heavier nuclei, but to those with a small neutron excess.

Figure 3 gives ground state isospin impurities based on this particle-hole scheme ' and on Hartree-Fock calculations 2) by Lee and cusson '. The comparison between nuclei in the valley of p-stability, where impurities level off at 1% or less, and mirror nuclei with N ~ Z is really striking, as is the suggestion that the latter's impurities could possibly reach IO56. With this picture in mind I should now like to discuss some specific experiments that reflect the importance of charge-dependent mixing. These will be studies of super- allowed p-decay. 1 shall begin by outlining the basic con- cepts involved in a description of the physical process. That will be followed by a summary of existing data with particular emphasis on our recent work not only at Chalk River but at Brookhaven and Michigan State university as well. Finally, 1 shall assess the data in an attempt to reconcile the known nuclear transition intensities with one another and, using the insight this affords into charge-dependent mixing, to place them in the context of weak interactions in general. The intensity of a nuclear p-transition is expressed in terms of an ft-value, which for superallowed decay between 0+, T = 1 states is given by^' ':

V

(lc)

where K = 1.23063 x 1O"94 erg2cm6sec. Here f is the statistical rate function, £ is the partial half-life for the transition. G ' is the effective vector coupling constant and Mv is the vector matrix element. By choosing 0 initial and final states, only the vector interaction can occur; so by neglecting the small correction terms AR, 8R and 6C, it can be seen that all such fjt values should be nearly equal.

In fact, the correction terms appear to be of the order of a percent. Radiative corrections result from inter- actions between the particles involved in p-decay and the electromagnetic field. It has been found-'' that a separation may be effected into 6R, the "outer" term and AR, the "inner" term where the former is model independent but does depend upon the and nuclear charge, while the latter

is model dependant and very sensitive to the nature of the

decay process and the role that the strong interactions play

in it. The correction 6 is a measure of how much the analogue

states actually differ from one another, and as such it depends

upon charge-dependent mixing. However, while it does include

the effects of mixing with states of the same as well as

different isospin, it is not sensitive to the total effect,

but only to differences between neighbouring nuclei.

Ideally it should be possible to use calculated

correction terms and from the measured superallowed transitions

determine an accurate value for the vector coupling constant of

nuclear p-decay, GV. Assuming the universality of weak inter-

actions, Gv is related through the cabibbo angle, 9 , to the

corresponding constants G and GR for muon and kaon decay respectively: (2a)

=. 11 eL . v _ V - V (2b)

The importance of accurately evaluating the charge-dependent mixing correction now becomes apparent, if we determine e v from eq.(2b) and use eq.(2a) to derive GV then the value of

AR can be established from eq.(lb) - providing the other correction terms, 8_ and &„, are known, we shall see later C i\ that from this procedure it is possible to study the nature of the weak interaction process, examining whether it is mediated by a vector boson and if so what limits may be set on the mass of the intermediate boson. In 1969 Blin-Stoyle reviewed progress in the study of superallowed p-decay '. The experimental ft values known at that time, after radiative corrections had been applied, are shown in Fig. 4. Evidently the points scatter over two or three percent, which is well beyond the quoted error bars, in attempting to understand the scatter, one must look to inadequacies in the radiative corrections, unexpectedly large charge-dependent effects (6C) - or simply experimental errors. It now appears that the latter probably played the largest role, but at the time the scatter provided impetus to consider 6C, the effects of which have not been corrected for in Fig. 4.

In the absence of detailed reliable calculations for 6c

Blin-Stoyle made the following argument: 6Q arises principally as a result of mixing the initial and final nuclear states with 8 other T = 0 and T = 1 states and to a lesser extent with T = 2 and T = 3 states; under these conditions 6 must always work to increase the measured ft value. Accordingly, the super- allowed decay of 2°Alm, which had the lowest accurately measured ft-value, was concluded to be least affected by charge dependence and, further, it was assumed that what effects remained could be neglected. A value for the vector coupling constant of nuclear (3-decay was then extracted directly.

That, of course, assumed a great deal, if the difference between the 2°Alm and -^Cl decays was to be explained by charge-dependent mixing alone, then 6 must be

~ 2% for the latter, and the largeness of this value made it seem unlikely that 6 would be zero for the former. could the outer radiative corrections, which depend upon the energy of the transition and the z of the nucleus, have been

improperly accounted for? At chalk River we approached the problem at this point with the idea that by measuring the

intensity of both superallowed decay branches in a single T = 1

isospin triplet, the differences between the mirror decays

could then be attributed solely to charge-dependent effects

since most of the uncertainties in radiative corrections would

disappear for comparison within a multiplet. This would

provide the only accurate means of investigating charge-

dependent mixing in these nuclei.

Figure 5 shows a portion of the nuclear chart in which

the stable nuclei between nitrogen and calcium are shaded; the outlined in solid lines are parents of the familiar decays already discussed. The nuclei in dashed outlines are the ones whose decays we have recently studied. For masses 26 and 34 - two of the most interesting cases - it is possible to make a mirror comparison within the multiplet.

All the Tz = -1 nuclei can be produced by (^He.n) reactions on stable targets but the big difficulty, which has prevented accurate decay studies in the past, is that at the required ^He bombarding energies many other activities can be produced. Without the removal of unwanted activities, absolute branching ratios could not be accurately measured. The fast gas transport system used in these experiments is illustrated in Fig. 6. Either solid or gas targets were bom- barded for a predetermined time, the recoil atoms being therma- lized by gas in the target cell „ Then, by means of remotely operated solenoid valves helium gas was swept through the chamber transferring the recoils through 1/4-in (i.d.) tubing to the counting cell^^. En route, the gas with various activities passed through several traps and filters which removed unwanted components and ensured that more than 75# of the initial activity in the counting cell was from the desired decay. The transit time for the 4m from target to counting cell was about 50 msec, after which the latter was valved off and counting was begun. A high "duty cycle" was maintained by refilling the target cell and bombarding while counting was in progress. Although the system works best with rare gases we have transported 22Mg, 2^Si and 5°S with the same ease as Ne and 10

•^Ar. As an example of the quality of the data, the Si and

^ Ar delayed gamma-ray spectra are shown in Figures 7 ant* 8 •

Note that in the latter spectrum the 665 kev and 2580 kev peaks correspond to 2.5# and 0.8# decay branches respectively. Life- times were obtained by recording successive spectra and analyzing the decay of individual gamma peaks. Branching ratios were determined by comparing the intensity of gamma-decay peaks to

that of the 511 kev peak from positrons which annihilated in

the walls of the cell. corrections were made for weak con-

taminant activities and for annihilation in flight. The

results for these two nuclei are given in the decay schemes

of Figures 9 anc* 10.

These schemes illustrate the difficulties inherent in

decay measurements for T = -1 nuclei o There are three quantities necessary for the determination of f_t-values: the

decay energy, the half life and the branching ratio. Since the T = -1 parent nuclei are farther removed from stable z targets, their masses and half lives are more difficult to

measure, but it is the branching ratio which presents the

most acute problems since it demands efficiency calibrations

and corrections to be accurate to the order of a percent. For

the Tz as 0 nuclei, spins of the available final states require the super allowed branch to be exactly 100$.

Originally ' we measured only the half lives and

branching ratios for 6si and ^\r. taking their decay energies

and those of their mirrors from the 1971 mass tables^. in

addition, the half lives for 26Alm and 5^cl came principally 11

10 11 from the work of Freeman e_t al. ' * at Harwell, using these data we obtained a 4.5$ discrepancy between the transition intensities in the mass-34 mirror decays. Since the magnitude of this discrepancy considerably exceeded all expectations, we decided to re-examine the results obtained from outside sources, First, D.E. Alburger and I remeasured12^ at Brookhaven the relevant half lives for the supposedly well- known T = 0 nuclei. The results pointed out all the frustrations contingent to measuring such numbers with an accuracy of better than a percent. Figure 11 shows plots of the measured half lives for Alm and ^ cl as a function of publication date with our measurements appearing as open circles. Obviously more measurements must be "wrong" than "right", and the previously accepted value for y cl was certainly among the former. More recently, at Michigan State University, we have remeasured the masses of the T = -1 nuclei ^' and once again z our preliminary results indicate a significant change from the accepted value for mass 34. in the meantime the Harwell group ) confirmed our new half life for ™cl and revised their own earlier mass measurement for that nucleus. All these changes have had the effect of reducing the asymmetry. What asymmetry might one actually expect? Let us write the wave functions for initial and final states as:

T=T z (3a)

Yf(Tz+l) = aoY v T=T +1 z 12 where Y corresponds to the predominant T = 1 analogue configu- rations and the other terms represent small admixtures. Here v stands for all quantum numbers other than isospin, and the coefficients a and b can be derived from first order per- v v turbation theory. "The value of | MJ (and 8c) is calculated directly from the relation

If we denote by the superscript "+" the positron decay of the proton-rich member of a T = 1 isospin triplet and by the superscript "-" the decay of the Tz = 0 member, then

where a * '(t) is related to a reduced matrix element by

„V E - E o v

Here v is the total charge-dependent potential. Notice

that 5 and 6 as well as the difference (mirror asymmetry)

between them depend upon terms that are squares of reduced

matrix elements; all three should be of the same order.

We have made detailed calculations of 6 in an c attempt at a consistent analysis of all known superallowed

decays-'7. We considered the effects of mixing with other

0+ states in the initial and final nuclei by bringing these states actively into the calculation through a matrix diagonalization procedure. The computations were carried out with the Rochester-Oak Ridge shell model code1^) operated in a proton-neutron, rather than isospin, formalism, A

Coulomb matrix element, evaluated using harmonic oscillator wavefunctions, was added to all the input two-body proton- proton matrix elements and in addition the single-particle energies for the proton orbits were shifted relative to the energies of the corresponding neutron orbits. The effects of a charge-dependent nuclear force were approximated by increasing all the neutron-proton input matrix elements ty 2%.

These calculations still assumed perfect radial overlap between initial and final states so the Fermi matrix element was recalculated using Saxon-Woods radial functions

for which spin-orbit and coulomb effects had been included and its asymptotic form determined by the experimental binding

energy, calculated corrections for several decays, including

the known mirrors are shown in Table I where 6R is the outer p -z.

radiative correction to order Z or (ref. 16), and 6c has been

broken up into a part caused by the non-zero radial overlap (sw)

and a part from charge-dependent configuration mixing (c+CDNF).

These corrections are all quoted in percent. Evidently 6c is

approximately half a percent, with a smaller calculated

asymmetry, certainly the observed asymmetries are now

consistent with the calculations as seen in the last column or

Table I. However a striking problem remains. The results of our 14 calculations, together with the most reliable data, yield the plot of ft. values shown in Figure 12. They are certainly more nearly in agreement than they were in 1969/ Yeta n average of p all data has an unacceptably large x , and there is a very decided difference between the low and high mass data. In 2 fact, if the last four points are omitted a normalized x of

~ 1 is obtained for the average. The calculated charge- dependent corrections are undoubtedly less accurate for the heavier nuclear since the model space was more severely

truncated but the 1$ discrepancy apparent in Figure 12 seems

rather large, is this simply another case of experimental

error or are we observing the increase in charge dependent mixing predicted earlier?

The importance of answering this question correctly

lies in the significance of the vector coupling constant to

the theory of weak interactions, if we accept the ft-value

characteristic of the lighter mass nuclei and use our cal-

culated 6 values G ' is determined to be G ' = (1.4129 ± -49 ~*> 0.0005) x 10 ^ erg cm'', if G and 0 are known the inner (X V radiative correction is given by n .2 H Gv (5a) V 2 GM cos e U. V

From the K^ decay the cabibbo angle may be determined using the relation

2 2 ° * ev (5b) However the result for 0v, and consequently AR, depends upon the form factor used in the analysis of the kaon decay, if the conventional Klein-Gordon (K-G) form factors are adopted then AR = 2.7 ± 1.0#; for Kemmer form factors AR = 0.8 ± 0.6%. The impact these values have on the theory of weak interactions is shown by Figure 13 where the calculated A R is shown as a function of the mass cutoff '. The parameter Q is the average charge of the fundamental isodoublet underlying current algebra with Q = 1/6, for example, in the quark model.

The "experimental" AR values are shown by bars at the left of the graph. A local weak interaction theory corresponds to the cutoff being equal to the nucleon mass; it is completely inconsistent with the K-G analysis and also outside the K limit. Any increase in the calculated 6 - which seems to be the most likely direction for that quantity to move - would increase A and worsen the disagreement. The most strongly indicated conclusion appears to be the need for a theory in which weak interactions are mediated by a vector boson. Obviously, accurate prediction of the mass of the vector boson depends upon a precise knowledge of 6 . The mirror comparisons I have described here provide the only direct experimental handle we have for examining charge-dependent effects, and their agreement with expectation now gives some hope that we are on the right track. However, until we can reconcile the data for heavier nuclei, where the mixing is presumably greatest, we must continue to doubt the results for light nuclei as well. Many mirror comparisons are possible, 16

though, for heavier nuclei - in principal, up to at least A = 100 - and from Figure J we might be led to expect asymmetries of the order of a percent or more. If a few of these can be reproduced by calculation, then we may, at last, believe the problem is solved. •There are some tantalizing hints of what we might expect to find with increasing A. Earlier I described how single state mixing could be measured by observing p-decay between 0+ states that are not analogues of one another. The -resui&s for **aH known cases ' are plotted in Pigura ih. since only one admixed state is involved in each case the percent mixing is small, but note how rapidly it seems to rise with decreasing neutron excess. (Needless to say, one cannot rule out mass or structure effects with such a small sample.) In the same vein, we have recently observed ' the decay of the heaviest known self-con jugate nucleus, 7'2 Kr. The decay scheme is shown in Figure 15. The measured log f_t values indicate all observed decay branches to be "allowed" by normal criteria so the states populated in ' Br have been assigned 1+. However, any one of these excited states could be 0+ if the ^2Kr ground state had an admixture of a few percent from a low-lying T=»l state. There must be many other ambiguous cases of this type in other nuclei where "allowed" logo's have been thought to preclude 0+ - 0+ decay, single-state mixing of a few percent seems unlikely - but for nuclei near the N=Z line it is definitely not impossible, without doubt, the total effects of charge-dependent mixing will reach that value for such 17 nuclei, so it is to heavy mirror nuclei that we may have to look for the best testing ground of our understanding of the nuclear charge and its influence on in general.

ACKNOWLEDGEMENTS

Parts of this report are based on work performed in collaboration with H. Schmeing, J.S. Geiger, R.L. Graham and

I.S. Towner (AECL) ; K.P. Jackson (University of Toronto);

D.E. Alburger (Brookhaven National Laboratory); and W. Benenson,

G. Crawley, E. Kashy and H. Nann (Michigan State university) . 18

References

1) J.M. Soper in Isospin in Nuclear Physics edited by

D.H. Wilkinson (North Holland Publ. Co.. Amsterdam, 1969)

pp.115-172 2) H.C. Lee and R.Y. Cusson, Annals of Physics T2 (1972) 353 3) I.S. Towner and J.C. Hardy, Nucl. Phys. A205 (1973) 33 4) R.J. Blin-Stoyle and J.M. Freeman, Nucl. Phys. A150 (1970) 369 5) A. Serlin, Phys. Rev. .164 (1967) 1767 6) R.J. Blin-Stoyle in Isospin in Nuclear Physics, edited by D.H- Wilkinson (North Holland Publ. Co., Amsterdam, 1969) pp.115-172 7) J.E. Esterl, R.G. Sextro, J.C. Hardy, G.J. Ehrhardt and J. Cerny, Nucl. Inst. and Meth. 9_7 (1971) 229 8) J.C. Hardy, H. Schmeing, J.S. Geiger, R.L. Graham and I.S. Towner, Phys. Rev. Lett. 29 (1972) 1021 9) A.H. Wapstra and N.B.Gove, Nucl. Data A9 (1971) 267 10) J.M. Freeman, J.G. Jenkin, G. Murray, D.C. Robinson and W.E. Burcham, Nucl. Phys. A132 (1969) 593 11) J.M. Freeman, J.H. Montague, G. Murray and R.E. White, Nucl. Phys. 69 (1965) 433 12) J.C. Hardy and D.E. Alburger, Phys. Lett. £2B (1972) 341 13) J.C. Hardy, H. Schmeing, W. Benenson, G. Crawley, E. Kashy and H. Nann, (to be published) 14) J.S. Ryder, G.J. Clark, J.E. Draper, J.M. Freeman, W.E. Burcham and G.T.A. Squier, Phys. Lett. B43 (1973) 30 15) J.B. French, E.C. Halbert, J.B. McGrory and S.S.M. Wong

in Advances in Nuclear Physics, edited by E. vogt and 19

M. Baranger (plenum press, inc., New York, 1969) vol.3 1$) W. Jaus, Phys. Lett. *K)B (1972) 6l6 17) E.S. Abers, D.A. Dicus, R.E. Norton and H.R. Quinn, Phys. Rev. l67_ (1968) 1461 18) S. Raman and N.B. Gove, phys. Rev. c7_ (1973) 1995 19) H. Schmeing, J.C. Hardy, R.L. Graham, J.S. Geiger and K.P. Jackson, phys. Lett, (to be published) Table i: Measured f_t values with calculated corrections and asymmetry

Nucleus ft(raw) 6R^ 5c* 6c* Jt(corrected) Mirror (sees) (SW) (C4-CDNF) (sees) asymmetry,

3047 ± 3 l• 57 0 .31 0.05 3084 ± 3 26Si 3012 ± 49 l.60 0•34 0.04 3049 ± 49 26 m -1 .0 ± 1.6 Al 3040 ± 3 1.61 0•25 0.07 3079 ± 3 ) 3037 + 25 1.68 0.48 0.13 3069 ± 25 -0.45 ± 0.85 to 3051 + 8 l .68 0• 38 0.23 3083 ± 8 } o

3t = ft (1 + 5R)(1 - 5c)

A = ft.+/ft.~ - 1 21

CHARGE-DEPENDENT MIXING

ISOSPIN MIXING

SINGLE - STATE MIXING

1*' T,Tz

Fig. 1: Schematic representation of the effects of charge- dependent forces on nuclear wave functions; the lowest-energy states of each isospin are shown as longer lines. Also indicated are two ways in which p-decay can be sensitive to these effects. T=Tz T = Tz T=Tz,Tz+l x

X

o P n (o) (b) (c)

Fig. 2: Wave-function components involved in charge-dependent mixing for even-even nuclei. 22

10

/""

Q- STABLE I CO

z a. en o m H-F CALCULATIONS FOR N=Z

0. ,,, 10 50 100 200 MASS-A Fig. 3: Ground state isospin impurities for even-even nuclei. The Hartree-Fock (H-F) results are taken from reference 2; all others are based on the particle-hole scheme described in reference 1.

3190

i

1 3100 . 1 i 1 • n \

i% 3050 -

1 1 DATA UP TO 1969 3000

i 1 I 1 0 30 40 in

Fig Experimental f_t-values, including radiative corrections, for superallowed 0+ - 0+ (T=1) transitions plotted as a function of A for the^nuclei involved. This represents the situation in 1969°). T*= I

20

Fig. 5: Section of the chart of the from nitrogen to calcium. Stable isotopes are shaded, isotopes in solid outline are parents of decays previously studied; those in dashed outline are Tz = -1 nuclei studied at chalk River.

tovDownpurap

Fig. 6: Drawing of experimental equipment. The remotely operated solenoid valves are numbered. Energy (MeV)

y-rays observed following /3-decay of2 S

100 ZOO 300 400 500 £00 700 800 900 1000

Fig. 7: Spectrum of B-delayed gamma rays from the decay of 2osi. The 24jyig target was bombarded by 12 Mev ^He particles.

Energy (MeV) 40 "17 10' /-rays observed following /T-decay of MAr

10"

o

no zoo sab «oo Channel

Fig. 8: Spectrum of fj-delayed gamma-rays from the decay of 5^Ar. The H2S target gas was bombarded by 12 Mev •^He particles. 5067 oy ^. 2.197 sec

.-- 0.4% 4.49 ± O.Ofl 2.072 V— 2.9% 3.830+ 0.021

>- 21.8% 3.535 ± O.OIB I £156

— 74.9% 3.485 ± 0.007 0.226 ~ PflOQ. I _ 46iec 26,

/

' 100 % LOG tl »3.4B9± 0.00 I

-4.004

Fig. 9: Decay scheme for the mass-26 isotriplet

6.043

LOGii 1.3% 343* 0.04

O.B% Ji3i O'.V

-Z.5% '.— 1.1 5 2'=0.Q7 94.3 % 3.48 I • 0 007 1569 sec

100% LOG (1=3.501*0 002

Fig. 10: Decay scheme for the mass-j4 isotriplet 26

6800 -

6600 u 2%

6400 r

- 6200

l600h

2%

1550

I500L- -^ 1350 1960 i970 PUBLICATION DATE

Fig. 11: Plots of the measured half lives of Al and ^ Cl as a function of publication date. The results of reference 11 are shown as open circles.

T 1\ r

3300]

3200 I -0- •-§ 3100

3000

2900 8 Ne 26Si MAr

10 20 30 40 50 A

+ Fig. 12: Plot of all current data on superallowed 0 - 0+(T=1) transitions. 3t-values have been corrected for fi and 6 . R 10 100 A (BeV)

Fig. 15: Calculated inner radiative corrections AR shown as a function of A the mass cut off and ~Q the average charge of the fundamental isodoublet underlying current algebra.

9 10 20 NEUTRON EXCESS - (N-Zl Fig Single state mixing measured by observing p-decay between 0+ states that are not analogues of one another1^). 28

_0+ 5057 167 SEC

Pig. 15: Decay scheme18) of 72Kr, Additional copies of this document may be obtained from Scientific Document Distribution Office Atomic Energy of Canada Limited Chalk River, Ontario, Canada KOJ 1J0

Price - $1.00 per copy

1904-73