Internal Conversion Processes and Radiation Strengths The

f Internal Conversion Processes and Radiation Strengths in the Radioactive Decay of Atomic Nuclei

Lennart Holmberg

Stockholm 1973

•iEj-^taUisít- -nfc- *. TZI-xa Internal Conversión Processes and Radiation Strengths in the Radioactive Decay of Atomic Nuclei

Akademisk avhandling som med tillstand av matematisk- naturvetenskapliga fakulteten vid Stockholms Universitet för vinnande av filosofisk doktorsgrad framlägges till 4 offentlig granskning i föreläsningssalen för fysik fredagen den 18 maj 1973 kl. 10.15

av Lennart Holmberg Fil. lie. Internal Conversion Processes and Radiation Strengths in the Radioactive Decay of Atomic Nuclei

Akademisk avhandling som med tillstSnd av matematUk- naturvetenskapliga fakulteten vid Stockholms Universitet för vinnande av filosofisk doktorsgrad framlägges till offentlig granskning i föreläsningssalen for fysik fredagen den 18 maj 1973 kl. 10.15

av Lennart Holmberg Fil. lie. i Internal Conversion Processes and Radiation Strengths in the Radioactive Decay of Atomic Nuclei

Lennart Holmberg

Stockholm 1973 A ,'V-f

The form of the present: the past. The Kent of the present: the future.

S. Weõres Contents

Preface 4 Outline of the thesis 6 1. Radiation strengths 8 1.1 Introduction 8 177 9 1.2 The 113 keV Ml + E2 transition In Hi 1.3 E2 transitions in 115In 10 iQfi 1.4 El transitions in Ba 11 146 1.5 Ml transitions in Eu 13 221 1.6 E2 transitions in FΓ 14 2. Internal conversion processes 15 2.1 The description of conversion electron directional correlations 15 2.2 E2 transitions 21 2.3 El transitions 25 2.4 Ml + E2 mixtures 30 2.5 EO + Ml+E2 mixtures 31 3. On the electron - gamma directional correlation method 33 3.1 Methods applied in the present work 33 3.2 Current developments 35 References 38 Acknowledge ;ments 42 Appendix 1 43 Preface

Radioactivity was discovered in 1896, by Becquerel. This was the first contact with the atomic nucleus, and may be regarded as the starting point of nuclear physics. Three different kinds of radiation were discerned, alpha, beta, and gamma raye. The gamma radiation was found to be of electromagnetic nature. Later it was shown that also "the discrete beta spectrum" was a manifestation of the electromagnetic interaction: by "internal conversion" the nuclear transition energy is transferred to an atomic electron.

Gamow, in 1931, surveyed the quantitative analysis of the electromagnetic observables [Ga3l]. It was regarded sufficient to consider radiation processes of electric dipole nature only. However, for Internal conversion an additional possibility of great Importance was observed, electric monopole transitions. These could proceed through the emission of atomic electrons penetrating the nuclear volume. The penetration effect in internal conversion was thought to be responsible for the order-of- magnitude difference generally found between experimental and theoretical internal conversion coefficients.

Later it was realised that transitions of higher multipolarlty could be of importance. In this case the rate of internai conversion should be, relatively, higher. Thus, the ratio between electron and radiation emission could be used to determine the multipolarity of a transition. Around 1940, another means of determining this multipolarity was discussed, namely from the directional correlation of two gamma quanta emitted in cascade [Ha40]. The study of correlations involving conversion electrons offered the possibility to determine also the parity change in a transition. von Weizsäcker pointed out that nuclear isomerism could be associated with nuclear states which could decay only through the ¿mission of quanta, or conversion electrons, of high angular momenta [vW36]. The determination of electromagnetic transition rates has since then been extensively used to obtain information on the nature of excitations in nuclei, and for testing nuclear modele. For instance, Mayer and Jensen concluded that the isomeric transitions provided the most convincing evidence for the spin-orbit coupling shell model [Ma55]. From the foregoing it should be clear that the knowledge of the internal conversion processes is of importance for the evaluation of absolute and relative radiation strengths. Further, the strength of penetration Internal conversion transitions is an independent measure of nuclear properties.

The evolution of experimental nuclear physics has been possible only through the development of new instruments and methods, which to a large extent has parallelled the general technological development of this century. For instance, modern fast electronics and detectors rely heavily on the solid state technology. The same is true for the computers which have become indispensable, for example, in the cal- culation of internal conversion coefficients, and in nuclear structure calculations.

It was stated, in 1963, by van Lieshout that "Nuclear spectroscopy has seen its first bloom" CvL63], However, it eeems that the field is still active, its extension to high-resolution methods and ln-beam spectroscopy, for instance, representing developments of great importance. - The present work, carried out during the past ten years, is an investigation of the radioactive decay of atomic nuclei, ft is con- cerned with internal conversion processes and radiation strengths. Outline of the thesis

The thesis consists of this Introduction and the following papers.

I V. Sergeev, J. Becker, L. Eriksson, L. Gidefeldt and L. Holmberg, Levels of 115In populated in the decay of 115mCd, Nucl. Phys. A202 (1973) 385.

II Chr. Bargholtz, L. Erlksion, L. Gidefeldt, L. Holmberg and V. Stefansson, Levels and transitions in Ba, Z. Fhys., in press.

HI L. Holmberg, V. Stefánsson, J. Becker and V. Sergeev, Transition probabü- 44f5 Ities In Eu, Z. Phye. 257 (1972) 101. IV B.-G. Pettersson, L. Holmberg and T.R. Gerliolm, Non-existence of dynamic 198 contributions to the 412 keV E2 conversion process in Hg demonstrated by a new experimental method, Nucl. Phye. 65, (1965) 454.

V L. Holmberg, V. Stefanseon and B.-G. Pettersson, Internal conversion of E2 transitions in 152Sm and 154Gd, Nucl. Phys. A96 (1967. 33.

VI L. Holmberg, V. Stefánsson, L. Eriksson and B.-G. Pettersson, Conversion 1G2 154 electron particle parameters of E2 transitions in Sm and Gd, Nucl. Phys. A166 (1971) 297. VII L. Holmberg, L. Gidefeldt, M. Gunnerhed and B.-G. Pettersson, Dynamic effects in the internal conversion of El transitions in 175Lu, Nucl. Phys. A96 (1967) 305.

VIU L. Holmberg, V. Stefánsson and M. Gunnerhed, Internal conversion of the 208 keV El transition in *77Hf, Physica Scripte, 4 (1971) 41. IX L. Holmberg, V. Stefánsson, J. Becker, Chr. Bargholtz and L. Gidefeldt, Internal conversion and radiative processes of the 113 keV Ml - E2 transition 477 in Hf, Physica Scripte 6 (1972) 177. X B.-G. Pettersson, L. Holmberg and T.R. Gerholm, Confirmation of the presence of E0 In direct competition with Ml and E2, Nucl. Phye. 65 (1965) 466.

XI v> Stefáneeon, L. Holmberg, U. Bäverstam, J. Becker and V. Sergeev, The EO component of the 689 keV 2» •* 2 transition in Sm, Nucl. Phys. A197 (1972) 315. Xn L. Holmberg and Z.H. Cho, A system for precise determinations of electron- gamma directional correlations« Nucl. Instr. 93 (1971) 353. xm L. Holmberg, N. de Sousa, B.-G. Pettersson and T.R. Gerholm, Effects of deviations from cylindrical symmetry in lens spectrometers used for electron- gamma angular correlation studies. US1P Report 73-04.

XIV V. Stefáneeon, L. Holmberg and B.-G. Pettersson, Electron scattering effects in angular correlations, Nucl. Instr. 106 (1973) 289. Radiation strengths

1.1 Introduction

Electromagnetic radiation is emitted as the result of a change in the state of oscilla- tion of a nucleón. Thus, the study of the electromagnetic transitions may yield Infor- mation about the nuclear wave functions. When the wave functions, and the electromagnetic operator, are known, the transition strength can, by use of results of quantum electrodynamics, be formulated in the following way

2L+1 T(L)" TTRf B(L) where the reduced transition probability for an electric transition, for example, is written as

,>*

Natural units are used, m = c ft = 1. Further, a designates the fine structure constant, and k is the transition energy.

However, in most nuclear modele the wave functions are not expressed by use of the ordinary coordinates. Then, the expression for the operator maybe more complicat- ed; the quasiparticle formalism is one example. Transition strengths large compared to the values for single particle transitions result when the motions of the particles are coordinated. These effects are accounted for in collective models, where the operators can be quite simple. Bohr and Mottelson [BO53] gave the following form for the electric operator in the unified description, considering collective and particle degrees of freedom

2K (J. __2_)rr l e AI/ i *LM 41T o

However, the collective coordinates a are not related to the ordinary coordinates in a trivial way.

The measurement of electromagnetic transition rates is often used for determining the general structure, rather than the details, of the collective wave functions. That is, the internal consistency of the models Iβ studied by testing the prediction of, for instance, intensity ratlos.

The inconsistency between experimental results and the selection and intensity rules in the rotational and vibrational models has shown that more refined treatments are necessary. Deviations of the nuclear wave functions from the model wave functions, and deviations of the form of the electromagnetic operators from that usually assumed, have been considered. These effects can only be understood when a microscopic theory is used. The application of the pairlng-plue-quadrupole model has been quite fruitful in describing the low-energy states in even-even nuclei, especially in so- called transition regions.

In this chapter measurements of lifetimes of excited nuclear states are described. From an experimental point of view, there is a close connection between these investigations and those summarised in the following chapter, on internal conversion processes. This is so because the radiation strength can only be derived from the value for the lifetime as long as the conversion coefficient is known, and because the mixing of multipolarlties, determined for instance from conversion studies, has to be known for the evaluation of the separate radiation strengths. Further, the lifetime is used in the evaluation of the penetration elements, specific for internal conversion transitions.

The lifetime measurements of this work are a part of a study where also intensity and directional correlation methods were applied. The radiation strengths deduced are used for a discussion in qualitative terms of the structure of the nuclear states, the degree of coherence in the states is investigated.

477 1.2 The 113 keV Ml + E2 transition in Hf In the present work lifetimes in the nanosecond region were measured. The technique used may be regarded as a fairly straightforward application of modern fast electronics. The method of analysis was, for lifetimes several times larger than that corresponding to the slope of the prompt curve, a direct determination of the lifetime from the slope of the delayed curve. In a few cases, the lifetime was evaluated by a convolution procedure, involving a least-squares fit by use of the prompt and delayed curves [Ba73]. 10

The lifetime of the 113 keV level is fairly long, and the measurement is not expected to be difficult. In the present work gamma - gamma coincidences were registered by use of two plastic scintillation detectors (paper K). The convolution method was used for the analysis. The result, T* = 490 ± 15 ps, is shorter than the result of several recent measurements.

The value directly determined from the eiope of the delayed curve was close to the result of the analysis. Then, the most obvious possible source of systematic errors seems to be an Inadequate time scale. Outside the scope of the present work, a case where a high precision is attainable was measured [Be73]. That is, the lifetime of 59 the 1292 keV level in Co. Beta - gamma coincidences were registered. The result, T, = 555 ± 7 ps, is in agreement with the average of two recent measurements, T¿ = 564 é 5 ps [Ar7l] and Ti= 538 ± 4 ps [Ga72]. Thus, an erroneous calibration is not indicated by a comparison with these results.

Accepting the present value for the lifetime of the 113 keV level, and the mixing ratio determined in the present work, the particle and collective gyromagnetic ratios may be derived from a measurement of the rotation of the gamma - gamma directional correlation pattern in an external magnetic field [Ma62]. The results are in good agreement with the theoratical predictions by Nilsson and his collaborators.

1.3 E2 transitions in 15In

The idea of coexistence in odd In (Z = 49) nuclei of spherical and deformed states has been advocated by Bäcklin and his coworkers, in spite of the closeness to the magic proton number Z = 50. A strongly enhanced E2 transition between the — and - states in In indicated a collective nature of these states tBa"67a]. Recently, independent support for the suggestion of deformation was found in a measurement 3+ of the static quadrupole moment of the - state [Ha70a]. A continuation of the sug- ¿ gested rotational band was sought for in the present work (paper I). The intensity of the 105 keV £+ - -+transition obtained is appreciably lower than that reported by other investigators [Gr66, Mo69] *. When this result is combined

* The intensities arrived at in the recent work by Ishii [ls73] are in good agreement with the present. 11

7+ with an earlier, indirect measurement of the lifetime of the - level (T< * 0.14 ns) [Bo7l], and the transition Is regarded as rotational, a lower value for the intrinsic 1+ 3+ quadrupole moment is obtained than that derived from the transition, Q * 1.7 b, compared to Q = 2.6 b.

A direct measurement of the lifetime of the -r level was performed by registering gamma - gamma coincidences in the decay of mCd (Fig. 1). The result, Ti * 57 ± 5 ps, implies a quadrupole deformation in good agreement with that obtained for the lower levels, Q « 2.7 ± 0.3 b. Thus, these data fit into a description 3+ 1+ 7+ of the T , ;r , and - levels as members of a rotational band. The intensity data 9+ indicate that also the 1418.0 - state is deformed, as the decay of this level occurs 7+ preferentially to the 933.6 - level.

1.4 El transitions in Ba 136 In Ba there occur several strongly retarded £1 transitions, depopulating levels which are described as two-particle states. In one case, the 273.6 keV transition, an M2 component was found by gamma - gamma directional correlation measurements [Gr60], Together with an upper limit for the lifetime of the 2140.5 keV level [FU673, this result indicated an enhancement of the M2 transition, in disagreement with the systematica for nuclei lacking a well developed deformation.

The lifetimes of the 2140.5 and 2207.5 keV levels, populated in the decay of Cβ, were measured in this work (paper U).

In the measurement of the 2140.5 keV state a NaI(Tl) - plastic combination was used for registering gamma - gamma coincidences. The 67.6 keV quanta were selected in the spectrum from the plastic detector. The 273.6 keV, or, in special runs, the 1235.2 keV photo-peaks were selected in the NalfTl) detector spectrum. The high- energy slope of the prompt curve was characterised by an apparent half-life of 0.3 ns, short enough to make feasible the determination o* die lifetime directly from the slope of the delayed curve. The result is T,= 1.6 ± 0.1 ns. This disagrees with the upper limit obtained by Fujioka et al. [Fu67Ü. However, these authors did not measure the lifetime directly but instead looked for its influence when the B - 273.6 y combination was registered. !

COUNTS.. (PROMPT) tISm Cd

* t,

i>7

i i i i i i i i i i i i i i 0.5 IS

Fig. 1 A typical record of the time distribution of the 484 - 934 keV gamma - gamma cascade in In. The lifetime of the 2207.5 keV level was measured by registering beta - gamma coincidences. A thin plastic scintillator was used for detecting the beta particles and a Nal(Tl) detector for the gamma radiation. The 340.6 keV photo-peak was selected in the gamma spectrum. The result is T± = 3.1 ± 0.1 ns, in good agreement with that obtained by Fujioka et al.

The reduced transition probabilities are deduced for the transitions depopulating the two levels by use of present lifetime and gamma - gamma correlation data. The M2 strength of the 273.6 keV transition is 0.003 ± 0.016 Weisskopf units. The structure 136 of states in Ba is discussed (paper II).

1.5 Ml transitions la Eu

The excited states of Eu form the simple sequence expected in an odd - odd nucleus where the proton and neutron can recouple to I,I -1,1 -2 ... The order g g g of magnitude of the strength of the magnetic dipole transitions connecting these states is expected to agree with the Weisskopf estimate, unless the transitions are retarded by an accidental cancellation. The result of lifetime measurements in the decay of 146Gd indicated that the 115.6 keV state had a lifetime much longer than expected, namely Ti = 0.8 ± 0.3 ns [Ko70].

Upper limits of the lifetimes of the 115.6 keV and 230.3 keV states were obtained by registering electron - electron coincidences (paper US). The components in the 1 -2 -3 -4 (g.s.) triple cascade can only be partly resolved. The upper limits for the lifetimes of the 230.3 keV 2~ and 115.6 keV 3~ states are T^ (230.3) s 165 and T, (115.6) ¿160 ps.

A finite strength of the 269.5 keV 1~ - 3~ cross-over transition was found by Avo- tina et al. in a conversion spectrum study CAV66]. The cross-over to Ml stop-over ratio was appreciably larger than the Weisskopf estimate. The 1~ - 3~ and 2~ -* 4~ cross-over transitions were sought for in the high-resolution gamma spectrum. No evidence was found for either of the transitions. However, the upper limit obtained is just below that corresponding to the conversion strength obtained by Avotlna et al.

The strengths of the Ml and cross-over E2 transitions were calculated by use of the extreme single-particle model. In all cases agreement between the theoretical values and the present experimental limits was found. 14

221 1.6 221 The nucleus 221Fr belongs to a region of transition nuclei, which has not been so well studied. The low-lying levels do not fit into a rotational pattern, and it has been suggested that the nucleus is weakly deformed. The present measurement of the lifetime of the 36.6 keV state was performed in order to investigate the degree of collectivity of the deexcltlng E2 (< 20 per cent Ml) transition.

As described in appendix 1, the measurement was performed by registering α-e coincidences. The result is Ti = 1.1 ± 0.1 ns.

When the 36.6 keV level is assumed to be deexcited only by a pure E2 transition, the present result corresponds to an enhancement relative to the Welsskopf estimate by a factor of 80. However, an unobserved transition may connect the 36.6 keV and 25.9 keV states, the enhancement factor is then reduced to about 60. In lack of more 221 detailed information on the levels and transitions in Fr, the interpretation of the present result can only be tentative.

Whereas rotational bands are observed in even - even Ra (Z * 88) nuclei, the Rn (Z =• 86) nuclei appear less deformed, ft is indicated by the present result that 221 Fr (Z • 87) belongs to the well deformed nuclei.

* This work has only been reported in the form of an abstract [HO73]. A more detailed account is given in appendix 1. I am indebted to my collaborators for their permission to use the results in this context. The investigation was possible thanks to the courtesy by Professor B.S. Dzhelepov. 15

2 Internal conversion processes

2.1 The deacrlption of conversion electron directional correlations

The description of the directional distribution of internal conversion electrons is closely associated to the theory of gamma radiation distributions. Whereas in the latter case a photon of angular momentum L is emitted, in the conversion process the corresponding angular momentum is, via an excitation of the electromagnetic field, transferred to the initially bound electron. The coupling between the angular momenta of the virtual quantum of the electromagnetic field, and the electron, in- troduces various angular momentum recoupling coefficients in the expression for the directional distribution of conversion electrons. In the concise formalism, given by Rose and his collaborators CRO52, BÍ53], all effects due to the conversion process are confined to factors that multiply the terms in the corresponding gamma radiation formulae. These factors are known as particle parameters, bi.(*L> w'L1). The expression valid for the directional correlation of a gamma - electron cascade is

W <6' yeX> - kevEenA k Pk

with (ex}=Cbk Fk(L> L> v y

26ebk(ffL,ff'L+l;X) , y

, Ig, y]

where 6 is the mixing ratio for the electrons,

a(ffL;X)

The definition of the gamma radiation mixing ratio 6 is discussed in the following. The a denote the conversion coefficients; the F coefficients, well-known from the gamma ray directional theory, contain angular momentum recoupling coefficients. For high transition energies the conversion process essentially occurs at distances 16 large compared to the wave length of the photon. As the process then occurs at "macroscopic" distances • the direction of the photon fully determines the direction of the emitted electron; the high-energy limit of the particle parameters is b. * 1.

The internal conversion process is most simply described in the approximation of a vanishing extension of the atomic nucleus. This assumption may appear reasonable, the nuclear volume being very small compared to atomic dimensions. The emission of a conversion electron arises as the result of an interaction between the excited electromagnetic field and the atomic electron, and the transition amplitude becomes proportional to the strength of the field. The amplitude for gamma transitions is a measure of the field strength. Then, the radiation and conversion probabilities are proportional, which is the basis for defining the "normal" conversion coefficient. Except for the dependence on the energy, multipolarity, and parity change of the transition the conversion coefficient depends only on electron wave functions. All nuclear information is already contained in the radiation transition strengths. The same Integrals of electron wave functions enter the expressions for the particle parameter and the conversion coefficient. Due to the coherent contribution in the directional distribution of different multipolarities, and the resulting interference term in the formula, the experimental particle parameters may be more useful than the conversion coefficients in the study of weak (L+l)/L admixtures.

In certain cases the finite nuclear size is of great importance, cf. the review by Church and Weneser [Ch60]. First, the so-called static effect will be mentioned. When the finite nuclear size is considered, the electron wave functions deviate from those in the pure Coulomb field. The difference in integrals of the finite size and point nucleus wave functions over the nuclear neighbourhood is then not necessarily negligible, due to the singularities that appear for certain angular momenta. The effect is large for Ml transitions, as the amplitude of the (dominating) si final state is large in the region of the origin. The effect of the finite nuclear size has in most cases been considered under the assumption of a spherical shape of the nucleus. As the main part of the finite-size effects originates from the removal of the singularities, the results for the Internal conversion coefficients are not dependent on details of the radius or density distribution of the nucleus. Thus, the finite-size effect is in first approximation "model-independent". However, this is not so when the deviation from spherical symmetry, described by magnetic dipole, electric quadrupole and 17 higher moments, is taken into account. These effects are expected to be small; recent results for the quadrupole perturbation are discussed in the following.

The so-called dynamic effect of the finite nuclear size may in special cases be appreciable; it depends sensitively on the nuclear structure. The probability for magnetic conversion may be expressed as

T MLJML)l V L(L+1)(2L + 1)

I, 1 and k are the nuclear spin, current, and transition energy; A (ML) is the vector multlpole potential, B.. an angular factor and R-, an radial integral of electron functions. The electron penetration function * contains integrale over the nuclear volume. Thus, whenever the contribution of conversion processes occuring in this small volume can be neglected, the probability of emission of conversion electrons becomes proportional to the corresponding gamma ray rate,

2 Ty (ML) 8ir« k j < f II I Tn • A (ML)|| i>| + 0(0?) + • • •

The importance of the process of emission of penetrating electrons arises «hen the normal process, occuring outside the nucleus, is strongly retarded. As an electron experiences a different electromagnetic field when within the nucleus, the penetration conversion may be unretarted and then appreciable, relative to the contribution from normal conversion. Formally, this may be seen from the conversion rate given above. When the first matrix element appears forbidden by some selection rule, the second matrix element may still be unaffected due to the powere of r contained in the function *. The most obvious example of a penetration effect is the oc- curence of electric monopole transitions. There is no corresponding EO radiation, and, hence, no effect on the extra-nuclear electrons. The conversion procese in this case takes place completely within the nuclear volume. Penetration effects are also known for several highly retarded transitions of electric and magnetic dipole nature. 18

A proviso for the determination of experimental penetration effects is that the values for normal conversion processes are known, with sufficient accuracy. When the present work was started, finite-size and "screening" corrected values were available for a limited range of Z-values. More recently much more complete tabulations have been accomplished, with the screening effects taken into account by self- consistent field calculations [Ha68a, Ha68b, Pa67]. Aβ mentioned in the foregoing, there are many higher-order effects which have not been considered in these calculations, and the over-all accuracy of the results must be regarded as open to experimental verification. In certain cases significant discrepancies between theory and experiment have been found, urging the theorists to even more careful calculations.

Pauli, and Hager and Seltzer have prescribed how the penetration effects may be evaluated in a very straightforward way» The nuclear structure dependence is contained in polynomials, simply multiplying the normal values for conversion coefficients and particle parameters. Comprehensive tabulations of the coefficients appearing in the penetration polynomials are given in ref. [Ha69] and ref. [Pa67l. The normal particle parameter is normalized in such a way that the coefficient for the zero-order term in the expansion of the directional distribution should be equal to 1. This means thpt the conversion probability enters the denominator in the expression for the particle parameter. The expression for the particle parameter has to be renoraalised when penetration effects are considered. For a pure multlpole transition the normal particle parameter (b2°) is modified in the following way

Vb2°Q^X) where Q (A) is the polynomial taking care of the anomalies in the coefficient, and

Q2 (X) is a factor pertaining to the particle parameter specifically.

In order to reduce the number of parameters to be determined from experiment, the penetration contributions are treated in an approximate way. For instance, Church suggests that the matrix elements arising in a series expansion of the function* should all be set equal [Ch66]. Further, he finds that for ML conversion, penetration contributions influence mainly transitions to the i • L - J, state. The radial matrix elements R.., valid without penetration, will then be changed to

T \ c> 19

SRü+CfiX for J.» L - Jj, and will remain unchanged for other values of J.. Hager and Seltzer use exactly the same expression for X (the explicit form given above applies to magnetic transitions only) [Ha69]. However, the arguing of these authors Is different. They set all terms except the lowest obtained In the power series expansion of the penetration matrix element equal to zero. (Except for El transitions where also the r term is considered.) Pauli, on the other hand, finds the coefficients in the expansion to be fairly independent on the initial state of the electron and keeps the sum of terms as a subehell-independent parameter. Hager and Seltzer, in their expression for the penetration parameter, keep the next Important term beyond the long wavelength approximation.

Conversion coefficients and penetration parameters may yield Information about nuclear matrix elements, also when penetration effects are absent. That is« through lhe dependence of the conversion quantities on the multipoie mixing radio, 6* . Infor- mation about the directional distribution may in this respect be superior to conversion coefficient data, not only through the larger sensitivity to small multipole admixtures, but also due to the sensitivity on the sign of the mixing ratio. However, there has been quite a lot of confusion concerning the definition of this sign. Recent- ly there have been nuclear-structure calculations expressing the magnitude and the sign of 6 in nuclear matrix elements, which has made a reconsidering of sign-con- ventions necessary. Biedenharn and Rose [Bi53] defined the mixing ratio so that it did depend on whether the transition happened to be the first or second component of a cascade,

where 1 = 1 or i = 3, and the intermediate state is always to the right. That is, a mixture of emission and absorption matrix elements is used. In thfs way the same formal expression could be used for A^y) of the first and second component. *

* The Biederiharn-Roae sign convention is used in this work, when no other refer- ence is given, üi the more recent papers the convention using emission matrix elements has been adopted.

.-'U .... 20

Rose and Brink CRO67] treated this matter from first principles, and gave formulas using absorption matrix elemente only. Other authors have used emission matrix elements [HaG8b, Be69]. Then, interference terms in the expression for A. of the first component are to be multiplied by a factor (-1) " , that is for the usual case of (L + 1)/L interference by a factor of -1. Of course, the same applies to a converted transition.

Aβ has been stressed in the foregoing, the internal conversion process has, so far, only been described in an approximate way. It may be appropriate to mention that the same holds true for the process of radiation, emitted from an atomic nucleus. One example of higher-order processes, which is connected with internal conversion, may be visualised by the diagram given in Fig. 2c. First, the corresponding dia- grams for gamma radiation (a) and internal conversion are shown (b). The process of emission of a photon by an atomic electron (c) due to the nucleus - electron interaction is a third order process. Thus, it can, in general, be neglected in comparison with the process of direct emission of the photon, which is a first order process. However, when the internal conversion probability is large, the influence of the electron shells on the emission of the nucleus may have to be considered. a.

Fig. 2 Electromagnetic deexcltation processes of atomic nuclei, cf. the text. 21

2.2 E2 transitions

The electric quadrupole transitions seem to be ideal for tests of the internal conversion process, without regard of nuclear-structure effects. This is so because there • » are many absolutely pure (2+ - 0+) or practically pure (4+ - 2+) transitions. The static effects of the finite nuclear size should be much smaller than for magnetic dipole transitions. Aβ the E2 transitions often are enhanced, relative to «ingle- particle values, also the dynamic finite-size effects may be supposed negligible. However, the picture emerging from a comparison between experiment and theory has not been so simple.

The anomalous E2 internal conversion coefficients in rotational 2+ •* 0+ transitions in rare-earth nuclei was surveyed by Subba Rao [Su60] and by Bernstein [Be62]. From comparison of B(E2) values obtained in Coulomb excitation and lifetime measurements, discrepancies in the total conversion coefficients of 10 - 20 per cent were found to occur frequently. Also, in measurements by the internal - external conversion method, the K conversion coefficient of the 412 keV 2+ - 0+ transition in Hg was found to deviate appreciably from the theoretical value. Later, precise determinations of subshell intensities established anomalies in ratios involving l>. electrons. When the present work was already started, disturbingly large anomalies were reported in studies of the K conversion particle parameter of rotational transitions in 152Sm and 154Gd.

As emphasised in the foregoing, the conversion coefficient and the particle parameter are complementary measures of the conversion process. In fact, as there are (at least) two final states, two transitions occur, described by different radial matrix elements. In order to evaluate these, two observables have to be determined, ft was found desirable to try to settle the question of the nature of the K conversion process 198 of the 412 keV transition in Hg by a measurement of the particle parameter, determined in a gamma - electron directional experiment (paper IV). The 676 - 412 keV cascade is weak and to some extent masked by beta - gamma coincidences. A precise and accurate technique had to be used for this measurement. This was the reason for developing the b. method. As shown by Biedenharn and

Rose [BÍ53] tlere exlüts an exact relation between bo and higher order particle parameters. Ft r the conversion of si and p¿ electrons the following relation is valid 22

b2=1.4-0.4b4

When b. can be determined with a precision comparable to that of bo, the errors 4 2 resulting by use of this relation are decreased due to the presence of the factor of 0.4. Even more important should be the possibility to appreciably reduce the influence of systematic errors. Especially for b4 0 relative errors in b. do not influence b2« Thus, the b^ method should make feasible the determination of precise, as well as accurate, values of bo. it The experimental value for b„, derived in the way described is given in Table 1, together with theoretical values, according to the table by Hager and Seltzer [Ha68b]. The analysis (paper IV, page 463) of the significance of the result in terms of dynamic effects is based on the formalism by Green and Rose, and may now seem ob- solete. If only the nuclear charge penetration is considered, X_ in the formalism by

Hager and Seltzer [Ha69], the result for bo infers X = - 5 ± 8. This corresponds -2 to a conversion coefficient a= (3.07 ± 0.10)10 when all deviations from the tabulated values are interpreted as due to penetration effects. The theoretical value for the conversion coefficient is OL. = 3.01 10~ [Ha68a]. Table 1 Experimental and theoretical K conversion particle parameters for E2 iftj) transitions in Pt and Hg E (keV) exp

78 (Pt) 333 1.473 ±0-010 1.455 356 1.423 ±0.010 1.428 80 (Hg) 412 1.32 ±0.04 1.345

The "normal" result for the conversion process studied in paper IV was presented at the Warsaw conference, where also two measurements of the conversion coefficient were reported. These were carried out by use of an improved internal - external conversion method [Be63] and a beta - gamma coincidence method [Le63], —2 —2 respectively, yielding (3.01 ± 0.07) 10 and (3.03 ± 0.05) 10 . Thus, a consistent picture emerged from these measurements.

The same technique of determining b„(E2) was used in paper X, for studying the E2 196 conversion process of the 356 and 333 keV transitions in Pt. The main purpose 23 of this paper, however, was to determine the electric monopole contribution to the 333 keV transition. As there are several parameters needed to describe the conversion process of this transition, the b. method is most useful for investigating the E2 component; the contribution of the EO and Ml componente to the fourth-order term of the directional correlation is confined to an attenuating factor in the denominator.

The experimental particle parameters are presented in Table 1, together with the theoretical values. In view of the agreement with the theoretical values, the possibility of dynamic contributions to the E2 conversion process is disregarded in the further analysis of the Ml and EO penetration effects.

Also Hamilton and his coworkers used the particle parameter as a tool for studying the E2 internal conversion process. For the 122 keV 2+ - 0+ and 245 keV 4+ - 2+ transitions in 152Sm, and the 123 keV 2+ - 0+ transition in 1S4Gd large deviations (~ 20 per cent) were found between the experimental and theoretical values [Ha65]. For the 344 keV 2+ - 0+ transition in Gd, on the other hand, perfect agreement with theory was obtained. The K conversion coefficients of these transitions did not exhibit any appreciable anomalies. This fact, however, may well be reconcilable with anomalous particle parameters. The large discrepancies reported by Hamilton et al. seemed worth further investigations. Again, the anomalies seemed tobe related to the nuclear deformation.

Paper V is an account of a measurement of the 4 - 2 ( Sm) and 2+ - 0+ ( Sm 154 and Gd) rotational transitions in these nuclei. The particle parameters were determined from the 1408? - 122K, 868y - 245K, and 1274y - 123K directional correlations, and the corresponding y - y correlations. By use of the b method a more precise value was obtained for the 245 keV transition (b„ = 1.76 ± 0.07) than that reported in ref. [Ha65] (bo = 1.07 ± 0.16; the theoretical value is 1.73). For all three transitions the results presented in paper V agree with the tabulated values. However, the matter of anomalous particle parameters could not be regarded as. settled. Nasir et al. [Na67] arrived at results for the 2+ -• 0+ transitions in very good agreement with Hamilton's. It was suggested by these authors that the gamma < gamma directional correlation results in paper V were in error (too low), yielding too large values for the particle parameters. Thus, the particle parameters of the 2+ -• 0+ transitions were reinvestigated by use of a more consistent and convincing 24

technique (paper VI). The b. method was applied, and the electron - gamma and gamma - gamme correlations were measured in effect simultaneously, in order to avoid any effects due to changes of extra-nuclear perturbing fields. A new instrument [Ge72], especially constructed for precise measurements of gamma - gamma direc- r tional correlations» was used for checking the gamma - gamma data. This instrument, the MCG, was also used to look for variations in the directional correlations, caused by changes of the gross surroundings of the source. Again, no discrepancies between the experimental results and the theoretical values were found.

In rare-earth nuclei the experimental L./L ratios are larger than the theoretical by about 5 per cent, cf. the survey in ref. CMa723. Mátese theoretically studied the influence of the static quadrupole moment on the L subehell conversion coefficients [Ma68]. The effects were found to be two orders of magnitude smaller than die experimental. Higher order processes involving two electrons (Fig. 3) were conslder- ed by Hager and Seltzer [Ha70b]. For the 100 keV E2 transition in W the effect

on the L./Lo ratio was found to be 5.6 per cent. It was remarked that the same processes could explain a deviation between experimental and tabulated values for the K particle parameter.

Fig. 3 An example of higher-order processes in internal conversion, involving two atomic electrons.

{»* A.*», 25

By now, many measurements of the 2+ - 0+ particle parameters in Sni and Gd have been performed. Koopmann and van Kragten [Ko69] discovered severe variations in the attenuation of the directional correlations when the gross surroundings were changed. This was the origin of the anomalies earlier arrived at by van Krug- ten [vK67]. Blanchard and Zganjar [B172] performed a similar study with sources earlier used by Hamilton et al., and confirmed the existence of this effect. No such effects were found for europium oxide sources, such as were used in the present experiments.

154 The recent results for the 123 keV transition in Gd all agree with the normal value for this particle parameter. However, for the equivalent 122 keV transition in 152 Sm the picture is less dear, as significant anomalies have been obtained by a few authors. Thus, the question of these suggested anomalies can not be regarded as completely settled, but the outcome of the present work indicates that when proper precautions are taken to avoid systematic errors, no deviations from the theoretical values are discernible, with the precision at present attainable.

2.3 El transitions

Penetration effects were discovered in many low-energy El transitions in heavy deformed nuclei. The method used in these investigations was the measurement of

L subshell ratios. The anomalies were found in the L. and Lo coefficients. An analysis showed thai the so-called nuclear charge matrix elemente would affect also the L conversion coefficient. This is not so for the nuclear current matrix element, o which, hence, should be dominating in these El transitions. Church and Weneser, and Kramer and Nilsson showed that this conclusion could be reconciled with nuclear models for these deformed nuclei. Also in rare-earth nuclei strongly retarded El transitions occur, suitable for investigations by conversion coefficient and particle parameter measurements. Two transitions of the spin-flip type in Lu were studied in this work (paper VII). The experimental value for the El particle parameter of the 10 times retarded 283 keV transition is 0.07 ± 0.13, to be compared with the theoretical value of -1.51. Also

' Kalfas et al. recently reported a value smaller than the theoretical by (8.5 ± 2.1) per cent [Ka73]. 26 for the mixed El - M2 particle parameter a significantly anomalous result was obtained, whereas no deviations from the tabulated values were discerned for the 145 keV transition. By use of the mixing ratios 6" (M2/E1) determined from a nuclear orientation experiment, and conversion coefficient data, the penetration matrix elements may be deduced. In the formalism of Hager and Seltzer we obtain for the nuclear-current and nuclear-charge penetration parameters (Fig. 4).

X. = -5.1 ±0.2 l -100 ± ICO

As will be discussed in the following, the nuclear-current matrix element is allowed according to the asymptotic selection rules in the Nilsson model [Kr62]. m order to verify that the nuclear-current matrix elements pertaining to the 396 keV and 283 keV transitions are related according to the intensity rule by Alaga et al. [A155], the semi-theoretical ratio between the penetration parameters is evaluated

X (283) d (396) 9/2 19/2 .-9/2 17/21 9/2 -17/2 '^9/2-17/2 = 0.37

The corresponding experimental ratio is

X4 (283) -0.42 ±0.03 ^(396) 177. For a parallel case, the 208 keV spin-flip transition in " Hf, a less clear-cut picture emerged. For the 321 keV transition, with a retardation factor of 6 10 , large penetration effects have been observed. The 208 keV transition is less retarded, 4 3 10 times, and definite penetration effects are neither observed in the subshell, nor in the directional correlation data (paper VIH). In fact, according to the intensity rule, the effect should be much smaller than in the 321 keV transition (with X. = 13 ± 3), namely |X.| = 0.4 ± 0.1. However, the subshell ratios and the particle parameter suggest different signs of the penetration parameter. Thus, in this case the sign of X. can not be deduced.

Generally it is possible to determine the sign of the radiation matrix element from the experimental value of the penetration parameter and the theoretical value of the (allowed) penetration matrix element. The sign of the radiation matrix element, forbidden by the Nilsson selection rules, should be of importance for comparison with more detailed nuclear structure investigations. 27

Fig. 4 Analysis of the internal conversion data for the 283 keV El transition in Lu. The result used for the electron - gamma directional correlation is that reported in paper VH. Conversion coefficient data by Emery and Perlman, and subshell ratios by Herrlander and Ewan, are used (references in paper VII).

The structure of the matrix element of the spin-flip transition is

It is evident that the gyromagnetic ratio g may be determined from the experimental matrix element. The effective value for this ratio is« from the transition« in Lu,

g =0.5g (free)

As remarked by Emery and Perlman [Em66] the value for the nuclear-current ma- 28 trix element can be used to evaluate the contribution of the corresponding radiation matrix element. That is. the contribution to the electric multipole radiation due to- the moving magnetic moment of the proton. This effect, in the present case, amounts to several per cent of the radiation amplitude.

173 Iα Yb there occur retarded El transition superficially similar to those discussed 173 in the foregoing. However, in spite of the fact that the 351 keV < Yb) transition is 17R 477 even more retarded than the 396 ( Lu) and 321 keV ( Hf) transitions, the K conversion coefficient seems to be unaffected by penetration effects. This difference may be understood in terms of the Nilsson model. In Table 2 are reproduced the selection rules on the asymptotic quantum numbers for the lowest order nuclear spin current matrix element [Kr62], Comparison between tables 2 and 3 directly 173 shows that the corresponding penetration transitions in Yb are not allowed by the selection rules. Consequently, it is not likely that even narrower limits of error than those arrived at in ref. [Ho653 would reveal any anomalies in the electron particle parameter of the 272 keV transition.

Table 2 The selection rules for the asymptotic quantum numbers in die Nilsson model, pertaining to the lowest order spin current matrix element

AK Operator AN AA AS

-1 z a ±1 ±1 -1 -1 o

- i y) a ±1 0 -1 o

0 (x - i y)

(x + iy)<7, ±1 0 +1 -1

+1 ±1 ±1 o •H

(x + iy)

173, 175 177, Lu Hf

Asymptotic quantum numbers Initial 633 T 514 t 624 I Final 512 t 404 1 514 1

I' - I + 1 transitions Energy (keV) 272 283 208 Hindrance factor 5.3 104 9.7 105 3.1 104 1.03 ±0.07 ** -0.05 ± 0.09 0.99 ±0.03

-Itransitions Energy (keV) 351 396 321 Hindrance factor 6.6 106 1.7 106 6.2 106 aexp/tt° 1.24 ±0.17 4.68 ±0.07 5.5 ±0.3

* From ref. [Ho7l] where references to the experimental date are given

** Ref. CHO65] 30

2.4 Ml + E2 mixtures

The El transitions in odd deformed nuclei discussed in the preceding section occur in cascade with rotational Ml - E2 transitions. The internal conversion processes 177 of these mixed transitions seem to deserve their own study. Especially in Hf, where the Ml component proceeds slowly, and the conversion process might be af- fected by nuclear structure dependent contributions. Further, investigations of the conversion process should be of value for the determination of the mixing ratio.

No unique mixing ratio could be deduced from the subshell measurements of the 113 keV transition in *' 'Hf [NO64]. The mixing ratio derived from several internal conversion observables [TÖ68] was not in accordance with the gamma - gamma directional correlation data. This inconsistency was confirmed In the present study (paper DC). The internal conversion data were analysed in terms of the penetration contribution to the Ml component, and the Ml - E2 mixing ratio. The y - » directional correlation results did not fit into the solution obtained from subshell «id gamma - gamma correlation data. The discrepancy between the present result for the y - K directional correlation, and the value expected from other observables, is not significant. However, the mutual agreement between the results of several experimental investigations makes it necessary to consider the possibility of an anomaly in the particle parameters.

Such an anomaly would in this case not be completely unexpected. The Ml - E2 particle parameter has a fairly small value, bo = -0.083. An error in the tabnistmf value may be small on an absolute, rafter than a relative scale. Thus me relative discrepancy could be an order of magnitude larger than for transitions with |b_ j = 1-2.

175 For the 114 keV transition in Lu differing values have been obtained for the correlations involving the K electrons. There is no discrepancy between the value given in paper VII and the theoretical value. It should be noted that the weighting of 477 175 the particle parameters is quite different in Hf and Lu, due to the different values of the mixing ratio 6 (E2/M1). 31

2.5 EO + Ml + E2 mixtures

The study of electric monopole processes by electron - gamma directional correlations is essentially confined to mixed transitions; the pure EO transitions have an isotropic distribution. The directional correlaticss are more sensitive than intensity \ data to small EO admixtures, due to the EO - E2 Interference term. Further, the sign of the corresponding mixing ratio c (E0/E2) can only be determined from the correlation data.

The EO transition strength, as well as the E0/E2 mixing ratio, Iβ a sensitive measure of the nuclear shape, and strongly model dependent, m the rotational model without rotation - vibration coupling one obtains for bete band to ground band transitions CKU73]

c 4eo MIÍT)

where the definition of «(E0/E2) is

(EO) e (E2)

The sign of c should be the same as the equilibrium deformation 0 , thus positive for a prolate and negative for an oblate nucleus.

This relation was checked by studying the directional distribution of the 2-2 152 ^ transition in the well deformed nucleus Sm (paper 3d). A large EO admixture was deduced [Ri69] from electron and gamma intensity data, even if no complete analysis involving the Ml admixture and its possible penetration effects was carried out. The positive sign of c obtained in the present work agrees with the rotational model prediction. However, the formula given above yields a magnitude which is far from the experimental. A collective model prediction in excellent agreement with the experimental value was obtained by Aveledo and Davidson [Av70] by including the fourth-order deformation, determined from inelastic scattering. Oα the other hand, the value obtained by Kumar CKU73] in a microscopic pairing-plus-quadrupole cal- culation seems to be too large. Due to the sensitivity on the nuclear shape, again a better agreement might be achieved by considering fourth-order deformations. 32

The mixing ratio c (E0/E2) is an important observable for testing the pairing-plus- 3. qoadrupole description of nuclei in the transition region A «a 190. A clear-cut ex- 186 perimental result was obtained in a study of the 333 keV transition in Pt (paper \), a classic case [Ge58, Ge62a3. By use of the theoretical coefficients by Hager and Seltzer, the E0/E2 electron amplitude is obtained as q * -0.25 ± 0.07.

Neither the rotational nor the vibrational model predicts an electric monopole component in this "2 - 2 " transition. However, the sign as well as the magnitude of the experimental mixing ratio, e = -0.015 ± 0.004, is well reproduced in the microscopic description by Kumar, c = -0.018 [Ku73]. 33

3 On the electron - gamma directional correlation method

3.1 Methods applied in the present work I The present work was carried out during the second decade of electron - gamma directional correlation measurements, of. the review in ref. [Ge7l]. However, the methods used were, in essence, conceived already during the first ten years. From the onset, the magnetic spectrometer was recognized as a superior instrument for the energy selection of the electrons. In fact, for some time the electron - gamma directional correlations were a necessary complement to the gamma - gamma cor« relations in the study of complex spectra, as the energy resolution of the magnetic spectrometers was superior to that of the Nal(Tl) gamma detector.

The magnetic spectrometer still seems to be the most versatile instrument for use in electron - gamma correlation measurements. The break-through in the development of solid state detectors for electrons has not influenced the directional correlation field to a very large extent. The better energy resolution, at high energies, of the solid state detector is counterbalanced by the limitation in counting rate, especially as the background effects may be severe. The possibility of multichannel registration of the electron spectrum is in practice often compensated by the corresponding change from multichannel to one-channel analysis of the gamma spectrum. The Gerholm magnetic lens spectrometer was constructed for use in coincidence measurements, where a high transmission is indispensable. The present investigations were performed with a copy of the spectrometer described in ref. [Ge62b]. For future applications the combination of magnetic selection and energy analysis in a solid state detector seems recommendable, especially at high electron energies.

Multbtatector operation is realised as an important way to speed up the otherwise tedio i c< toting of coincidences for directional analysis. However, the true MCG cone» ;>t [^©72] can not be accomplished with a system equipped with electron and gamma detectors. So far, most measurements have been performed by use of only two detectors, one of them movable.

Systems with several electron detectors have been constructed, for instance by Siegbahn et al. [Si63], and also systems using more than one gamma detector. 34

Some advantages of a three-detector setup for simultaneous measurements of electron - gamma and gamma - gamma directional correlations are discussed in paper Xu. They encompass the possibility to use the same analysing system for the f gamma component appearing in both the electron - gamma and gamma - gamma cascades, and the Independence on changes In the gross structure of the source during the course of measurements. The variation in detection efficiency with the position of the movable gamma detector is not always easily determined. It is shown that errors in the normalisation constants, caused for instance by variation in the photomultipUer amplification with the position, or by scattering, can be appreciably reduced by choosing the appropriate position for the second, fixed gamma detector. The difficulty of finding proper normalisation factors is encountered for instance when the common gamma transition is of low energy in a complex spectrum. In the 477 application of the three-detector system to the 208 - 113 keV cascade in Hf the precision attained was almost an order of magnitude higher than that reported earlier. As mentioned in paper DC similar advantages are arrived at when the moving NaI(Tl) detector is replaced by a high-resolution Ge(Li) detector. Ge(Li) detectors, with an efficiency comparable to that of Nal(Tl) crystals of the size generally used in directional correlation studies, are now commercially available. The combination of a magnetic lens and a Ge(Li) detector offers special advantages due to the good energy resolution in both channels, and the lack of interdependence between the detectors. Such a system should be especially useful for studies of complex gamma spectra in coincidence with a highly converted transition, for instance the 2+ — O+ rotational transitions in heavy nuclei.

The b. method, used in four of the investigations (paper IV, V, VI and X), was described in the foregoing. The original baffle system of the spectrometer was not op- timised for the determination of fourth-order terms. Thus, new baffles with a smaller take-off angle of the electrons were designed. By use of this system the statis- tical errors become smaller, and the result is not so dependent on systematic er-

rors in the value for the solid-angle correction factors. A P4 (cosO)-shaped mask wee used for measuring this factor i^, in analogue to the Pecoso) method given by Gerholmetal. [Ge62b]. 35

Ás the fourth-order directional correlation coefficients often are smaller than those of second order, they should be more sensitive, relatively, to systematic errors resulting in a deviation of given magnitude from the true value of the coefficient. Á possible source of such errors is the deviation from cylindrical symmetry exist- ing in all spectrometers i The effect of asymmetries on the electron - gamma directional correlation was studied in paper XIII. Asymmetries causing an "effective misalignment" are most severe; that is effects appearing when the "center of efficiency" is not on the nominal axis of the spectrometer. Only misalignments with a component in the directional correlation plane contribute to first order, and these are easily revealed by measuring the coincidence counting rate at the relative angles of 135° and 225°. Aβ shown in paper XIII even unrealistically large deviations from symmetry will yield moderate errors in the correlation coefficients.

The interaction of electrons with dense materials results in a scattering effect which may be disastrous unless special precautions are taken. The influence of scattering is, in general, avoided by resorting to the use of very thin sources. When correc- tions caused by source thickness have been discussed, most investigators have re- ferred to the theoretical investigation by Frankel [Fr5l]. However, these results have not, to a very large extent, been tested experimentally. The investigation described in paper XIV may be regarded as such a test. Further, it is suggested that the scattering can be related to a directly measurable quantify, the energy loss of the electrons. In this way the difficulty to determine the thickness of the source is circumvented. However, it is shown that the scattering can not be defined unambig- uously. Depending on the energy resolution, and the geometrical properties of the spectrometer used, different effects may result.

3.2 Current developments

The introduction of high-resolution Ge(Li) detectors for the registering of gamma radiation has opened new possibilities in the field of electron - gamma directional correlations. However, for studies of the internal conversion process, an increase of the resolution in the electron channel would be of primary interest. Attempts have been done to use doublefocussing magnetic spectrometers in combination with Nal(Tl) detectors [An70]. The development of solid state detectors with a resolution of ~ 0.1 keV at 100 keV would be an interesting alternative. 36

An example of applications of electron - gamma setups with good resolution in the electron channel is the study of L subshell particle parameters of pure E2 transitions. Information about these particle parameters would be an important complement to the subshell ratio data. Also for the study of nuclear penetration effects the L subshell particle parameters are of great interest.

The electron - gamma directional correlation method is certainly limited by the re- striction to cascades with a fair anisotropy. The study of the directional distribution of electrons emitted from oriented nuclei would greatly increase the number of cases that can be studied (an example was mentioned in paper VII, the study of penetration effects in the cross-over El transition in Lu). A pioneering experiment of this kind was performed by Frankel et al. [Fr64], who used adiabatic cooling. The introduction of dilution refrigerators has since then increased the versatility of the directional distribution method. The application to the study of transitions which are essentially totally converted is being explored by the Leuven group [Si73 j.

A few experiments on the directional distribution of conversion electrons emitted in nuclear reactions have been carried out. The group at INS, Tokyo, uses a magnetic spectrometer in mese studies [Ej66]. However, the directional distribution of electrons emitted from a recoiling atomic system in an ionised and excited state is not related to the nuclear parameters in a trivial way. In fact, this problem is related to the "hot atom chemistry" where so far a lot of experimental and theoretical work remains to be done.

The study of recombination effects ("after-effects") belongs to the same field. The electron - gamma method has been used for the study of the effects following internal conversion and electron capture processes LBä67b, Th7l]. There are several other examples of the application of the method to extra-nuclear effects. Whereas an external magnetic field disturbs the electron orbits, the use of internal magnetic fields makes the electron - gamma directional correlation method suitable for the determination of nuclear magnetic moments [De7l].

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P. Kleinheinz, L. Samuelsson and K. Siegbahn, Nucl. mstr. 32 (1965) 1.

Si73 R. Sil verane, private communication.

Su60 B.N. Subba Rao, II. Nuovo Cim. 17 (1960) 189.

Th71 J.E. Thun, in Angular correlations in nuclear disintegration, ed. by H. van Kragten and B. van Nooijen (Wolters-Noordhoff Publishing, Gro- ningen, 1971). TÖ68 S. Törnkviet, S. Ström, J.E. Thun, V. Schmidt and N. Baade, Nucl. Phys. A117 (1968) 336.

vK67 H. van Kragten, Thesis, Technological University, Delft (1967).

vL63 R. van Lieshout, Opening speach, International summer course in nuclear spectroscopy, Breukelen, Netherlands, July 30 - August 17, 1963.

vW3C C. F. von Weizsäcker, Naturwissenschaften 24 (1936) 813. 42

Acknowledgements

The experimental investigations described in the thesis were performed at the Institute of Physics, University of Stockholm. Professor T.R. Gerholm, head of V the nucleur physics group at the Institute, has been supervisor of this work. With- L^ out his Inspiration the work would not have been started, much the less completed. From the onset Professor B.-O. Pettersson was a friendly and generous teacher. The wholehearted support, and the guidance and criticism, by Professor Gerholm and Professor PeUersson during all phases of the work was indispensable; it has been a privilege to work with these two pioneers in the field of electron - gamma directional correlations.

V. Steftnsson was a most able collaborator, and the many years spent together was a very pleasant experience. The cunning contributions by J. Becker were essential for the recent developments of the experimental setup. Chr. Bargholtz, J. Becker, U. Baverstam, Z.H. Cho, L. Eriksson, L. Gidefeldt, M. Gumerhed, V. Sergeev, N. de Sousa, and V. Stefánsson offered a very stimulating collabora- tion, and their insight in physical problems has been invaluable. Many others, members of the nuclear physics group and other groups at the Institute, have contributed.

It seems appropriate to acknowledge illuminating discussions with a number of theorists in the field of internal conversion.

I am grateful to the personnel in the offices. C. Wallen», head of the mechanical workshop, was always willing to assist, and K-G. Andersson, S. Hübenette and K. Schmidt skillfully constructed the new directional correlation table for the Ge(Li) detector.

I. Gudlaugsdâttir made many of the ink drawings, and I. Wallin helped with the typing.

ft is a great pleasure to express my sincere gratitude to all these, who by their cooperation made this work possible.

Stockholm, March 1973.

=>*ifU- -5* . .U 43

Appendix 1

221 The lifetime of the 36.6 keV level in "*Fr 221 The nucleus Fr lies in an intermediate region, between spherical and deformed nuclei. The Influence of the unpaired proton on the onset of the static deformation should be revealed by the study of odd-Z nuclei. So far, there is comparatively little Information available about the odd-Z nuclei in this region. The lifetime of the 218 keV state in 217At Implies an enhancement factor of 40 for the deexciting E2 transition which may be regarded typical for a vibrational nucleus. On the other 227 hand, several rotational bands are observed in Ac.

22fi 221 221 Dzhelepov et al., who studied the decay of Ac to Fr, concluded the Fr is weakly deformed '. Several of the low-lying excited states of the same parity were associated with the Nilsso& states of negative parity in this Z-region. Some levels of opposite parity were suggested to form the beginning of a rotational band. at A conspicuous feature of the level scheme has been pointed out ', the occurrence of two levels at 36.6 and 38.4 keV, depopulated by E2 (* 20 per cent Ml) transitions to tho ground state. The lifetime of the 36.6 keV state is measured in this work. 225 The activity of Ac was produced at Dubna by irradiating a thorium target with 660 MeV protons. After chemical separation the source was prepared by evaporation 2 on an aluminium coated mylar foil, 1 mg/cm thick.

The lifetime was measured by registering alpha - electron coincidences. A Gerholm 3) magnetic spectrometer ' was used for selecting the conversion electrons, and the alpha-particles were detected in an NE 102A disc scintillator, placed close to the source.

The energy resolution obtained, 2.5 keV FWHM at 32 keV, was not sufficient to re-

solve the 36.6 M (mainly M£ + Mg), 38.5 M (M2 + Mg), 36.6 N + O, and 38.5 keV N + O complexes from each other. However, it should be possible to determine the lifetime of the 36.6 keV level without decomposing the time-distribution curve, by choosing a current setting of the spectrometer corresponding to the low-energy side of the 36.6 M peak; this transition is stronger by a factor two than die 38.5 M transition. A prompt curve approximately valid for the 36.6 M electrons (E ** 32 keV) Í:."U-Í)ÍÍ-'--I=Í=

44 was obtained by registering a - 62.9L coincidences (E « 44 keV), solectlng the same part of the pulse spectrum from the detector in the electron spectrometer as when registering the ot - 36.GM coincidences; separately it was shown that the lifetime of the 99.4 keV level, depopulated by the 62.9 keV transition, is shorter than

.* that corresponding to the elope of the prompt curve obtained in this way. The slope of this prompt curve is characterised by 1% = 0.22 ns. The result for the lifetime, derived from the slope of the delayed curve, is T, = 1.1 ± 0.1 ns.

For the following discussion it is assumed that the 36.6 keV transition is pure E2, as a competing Ml component, if present, would be dominating if not retarded by an accidental cancellation. It should be kept in mind that the experimental limit of the relative Ml admixture is 20 per cent.

Another, more severe, uncertainty is due to an unobserved transition which should connect the 36.6 or 38.5 keV states with the 25.9 keV state 4). The strength of this transition should be 30 per cent of that of the 36.6 keV transition.

The enhancement factor of the 36.6 keV E2 transition, with respect to the Weisskopf estímate, is about 80 or 60, for a 0 per cent and 30 per cent relative strength of the 12.6 keV transition, respectively.

221 As the information available concerning the properties of states in Fr is relatively scarce, no detailed interpretation of the present result in the framework of a nuclear model is possible. The following comments should be regarded as specula- 3 5) tive. When the spin of the ground state is assumed to be — , and that of the 7 3 36.6 keV state -, the formula pertaining to a K = — rotational band may be used to ¿ 2 deduce the static quadrupole moment, Q . The result is Q =6.9b, or Q^ = 6.Ob, for the 0 per cent and 30 per cent alternatives. This may be compared with the ~~ 220 222 quadrupole moments obtained from the B(E2) values for ' Rn, Q ^ 4.8 b and 22 224 22ft 228 R\ i for "•"'*>"°>'" °Ra Qa 6,2 b '. Thus, the Z-region 86 - 88 is characterised by an appreciable increase of the (static or dynamic) quadrupole distortion. The large E2 transition strength found in this work is typical for a well deformed nucleus. The non-appearance of a rotational pattern among the low-energy lévele of 221 Fr may be due to the presence of several particle states, and a strong interaction between the single-particle and collective motions. Further experimental and theoretical inveetigations seem necessary for elucidating the structure of nuclei in this transition region. A i i i

K>* • 36.6M a * 6B»L a

I I 1 I I I I TIME ft»)

225 Fig. Al A time distribution obtained by selecting M electrons of the 36.6 keV transition, and a particles» in the decay of Ac. The 62.9 L - a distribution should yield on approximate prompt curve. 46

References

1. G.D. Alkhazov, Yu.K. Zalite, M.L. Andersen and O.B. Nielsen, Zh. Eksp.fc Teor. Fiz. Pis'ma 12 (1970) 7.

2. B.S. Dzhelepov, A.V. Zolotavin, R.B. Ivanov, M.A. MikhaUova and V.O. Sergeev, Izv. Akad. Nauk SSSR Ser. Fiz. 33 (1969) 1607.

3. T.R. Gerholm i R. Othaz, and M.S. El-Nesr, Ark.Fys. 21 (1962) 253.

4. B.S. Dzhelepov, A.V. Zolotavin, R.B. Ivanov, M.A. Mikhailova, V.O. Ser- geev and M.I. Sovtsov, Izv. Akad. Nauk SSSR Ser. Fiz. 34 (1970) 2127.

5. L. Peker and Yu.P. Voronkov, Izv. Akad. Nauk SSSR Ser. Fiz. 34 (1970) 2096.

6. P.H. Stelson and L. Grodzins, Nucl. Data Ai (1965) 21.

<*-., J *-'

•<*». i I

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