the first reaction and by detection of evaporated neutrons in the second. Gamma ray spectra were collected in coincidence with these triggers using

Transcription

1 ABSTRACT Broken Reflection Symmetry (And Isospin Dependence of Enhanced El Transition) In 114Xe Steven Louis Rugari Yale University 1992 We have carried out a search for broken reflection symmetry in the exotic nucleus 114Xe. Evidence for broken reflection symmetry has been previously observed in the actinide region, most notably Ra-Th nuclei, and more recently in the neutron rich nuclei 144Ba, 146Ce, and 146>148Nd. This evidence has been discussed in terms of two conceptually different theoretical frameworks, namely alpha clustering and octupole deformation. The alpha clustering model makes global predictions of the relative strengths of enhanced electric dipole (El) transitions characteristic of broken reflection symmetry, and predicts a dependence on isospin divided by nuclear mass (N-Z)2/A2 of the reduced transition probability, B(E1), where A is the nuclear mass number and N and Z are, respectively, the neutron and proton number. The nuclei studied previously have approximately the same value of (N-Z)2/A2 between and In 114Xe this parameter is much different, (N-Z)2/A2 =.0028, allowing for a test of the prediction. On the other hand, the octupole model description is less straightforward. Two terms contributing to the calculation of reduced transition strengths are based on the collective liquid drop model of nuclei and have a global dependence on A2Z2. A third term, however, depends explicitly on the shell model description of the valence nucleons and can be large enough to remove this global dependence. The nucleus 114Xe was produced in the heavy ion fusion evaporation reaction 60Ni(58Ni,2p2n)114Xe in two separate measurements at Daresbury Laboratory and at Yale University. The nucleus was identified by means of a recoil mass spectrometer in

2 the first reaction and by detection of evaporated neutrons in the second. Gamma ray spectra were collected in coincidence with these triggers using similar gamma detector setups. Information on the angular distributions of the gamma rays was collected for at least three separate angles in each measurement. We have constructed the level spectrum of 114Xe from these measurements up to spin and parity 10+ and excitation energy of about 3 MeV. The spectrum shows evidence of broken reflection symmetry in structure and in extracted B(E1) transition strengths. The extracted reduced El transition strength has been compared to that in all previously studied nuclei exhibiting broken reflection symmetry and has been found to scale qualitatively according to (N-Z)2/A2, as predicted by the alpha cluster model.

3 B r o k e n Reflection S y m m e t r y ( a n d Isospin D e p e n d e n c e of E n h a n c e d E l Transitions) in * X e A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy By Steven Louis Rugari November 1992

4 to my parents, my brother Tony, my sisters Janice and Linda, and most especially to Angie

5 ACKNOWLEDGMENTS The work presented in this thesis would not have been possible without the help of many people. I am deeply indebted to Professor Moshe Gai who first got me interested in Nuclear Physics and has been my advisor throughout my graduate career. I have learned much from him about physics and about doing physics. I would like to thank Professor D. Allan Bromley for his continuing concern and talks about physics and my future career choices. I also appreciate all the work he and Professor Peter D. Parker have done to secure funding for the tandem Van de Graaff accelerator at Yale. Also, I would thank Dr. Hendrie and the USDOE for creating the necessary funding pool for equipment, without which the Yale neutron ball would not exist. I am very grateful to Professor Peter D. Parker also for the many times he has stopped to offer suggestions, to offer advice, to talk about physics, to help with equipment and administrative procedures, and to take time to thoughtfully answer innumerable questions. I appreciate the many insightful comments and advice I received from my committee members: Professors Gai, Parker, Firk, Alhassid and Schmidt. They all helped me to present the physics ideas more clearly and to make this dissertation more readable. I have also benefited greatly from discussions with and help from all the professors at the Wright Nuclear Structure Laboratory: Professors CJ. Lister, P. Chowdhury, S. Kumar, A.J. Howard and C. Bockleman. I greatly appreciate the time they have spent with me. Thanks are also due to the staff of the laboratory and all the time and effort they have expended to ensure its smooth functioning. In particular, I am indebted to: Joe Cimino, Tom Leonard, Ray Comeau, and Al Jeddry for their aid in building detectors,

6 beamlines, and all the apparatus necessary to performing experiments using the ESTU tandem Van de Graaf accelerator, John McKay and Richard Hyder for overseeing the construction and smooth operation of the accelerator, Jeff Ashenfelter, Kenzo Sato, Ted Duda, Phil Clarkin, Bob McGrath, Walter Garnett, and Bill Schief for operating the accelerator, Tom Barker and Dick Wagner for all their help in understanding, designing, and building the electronics and their extensive work on the accelerator control systems, to John Baris and Allen Ouellette for obtaining, maintaining and continually upgrading the Laboratory's computing and data acquisition systems. Many thanks are in order to Dee Berenda for drawing many of the figures, not only in this text but also in talks I have given, and also to Mary Anne Schulz, Rita Bonito, Lisa Close, and Karen DeFelice who keep the Laboratory running on a daily basis and have been of incalculable assistance in helping me to keep in line with the University. Lastly, I extend my appreciation to all the postdoctoral and graduate students with whom I have worked, studied, and learned in my years at Yale: Chris Winter, Sean Freeman, Stephen Sterbenz, Paul Cottle, Laurie Baumel, Patty Blauner, Kevin Hubbard, Michael Kaurin, Tzu-Fang Wang, Paul Magnus, Michael Smith, Kevin Hahn, Sinan Utku, Nick Bateman, Joe Germani, Craig Levin, Daniel Blumenthal, Patrick Ennis, Vicki Greene, Jeff Mitchell, Ben Crowell, Felix Chan, Nicholas Kaloskamis, Stuart Smolen, Heping Li, Stuart Henderson, Bernard Phlips, and most especially to those with whom I have worked directly: Zhiping Zhao, Brian Lund, Ralph France, Sumit Sen, Geoffrey Furnish, Sarah Gille, Peter Schiffer, and Alexa Harter.

7 TABLE OF CONTENTS CHAPTER I INTRODUCTION... 1 CHAPTER II THEORY OF BROKEN REFLECTION SYMMETRY II. 1 ALPHA CLUSTER MODEL SPECTRUM GENERATING ALGEBRA INTERPRETATION OF 114Xe LEVEL SPECTRUM 31 CHAPTER III EXPERIMENTAL PROCEDURE GENERAL OVERVIEW THE POLYTESSA DETECTOR ARRAY THE DARESBURY RECOIL MASS SEPARATOR THE YALE NEUTRON BALL CHAPTER IV DATA ANALYSIS IV.l LEVEL SPECTRUM OF 114Xe 60 IV.2 ANGULAR DISTRIBUTION IV.3 MIXED MULTIPOLARITY OF THE kev TRANSITION IV.4 TRANSITION RATES AND REDUCED NUCLEAR MATRIX ELEMENTS CHAPTER V DISCUSSION OF RESULTS V.l B(E1) SPIN DEPENDENCE V.2 El TRANSITIONS IN THE ALGEBRAIC MODEL 82 V.3 THE ALPHA CLUSTER MODEL V.4 SUM RULE MODEL v

8 V.5 THE OCTUPOLE DEFORMATION MODEL V.6 GLOBAL MASS AND ISOSPIN DEPENDENCE OF El TRANSITIONS CHAPTER VI CONCLUSIONS APPENDIX SCHEMATIC OF ELECTRONICS REFERENCES vi

9 TABLE OF TABLES TABLE 1.1 EXPERIMENTAL B(E1)/B(E2) RATIOS IN REFLECTION ASYMMETRIC NUCLEI TABLE 3.1 NEUTRON BALL DETECTOR PARAMETERS TABLE 4.1 ANGULAR DISTRIBUTION COEFFICIENTS FOR GAMMA RAY TRANSITIONS IN U4Xe TABLE 4.2 REDUCED MATRIX ELEMENTS IN 114Xe TABLE 5.1 EXPERIMENTAL B(E1)/B(E2) RATIONS INCLUDING 114Xe... 90

10 TABLE OF FIGURES FIGURE 1.1 VARIOUS NUCLEAR MULTIPOLE SHAPES MESON SPECTRA AND QUARK STRUCTURE BARYONIC SPECTRA AND QUARK STRUCTURE REDUCED ALPHA PARTICLE DECAY WIDTHS FIGURE 2.1 GEOMETRY OF ALPHA CLUSTERING IN NUCLEI SGA SPECTRUM FOR 0(4) SYMMETRY SGA SPECTRUM FOR U(3) SYMMETRY EXPERIMETAL AND THEORETICAL SPECTRA FOR C02 (COUPLED U(4) SYMMETRY) COMPARISON OF EXPERIMETAL AND VIBRON MODEL SPECTRA FOR 226Ra FIGURE 3.1 LEVEL SPECTRA OF THE LIGHT Xe ISOTOPES THE POLYTESSA DETECTOR ARRAY GEOMETRY DARESBURY RECOIL MASS SEPARATOR CROSS SECTION VIEW OF A HPGe DETECTOR AND COMPTON SHIELD TYPICAL COMPTON BACKGROUND SUPPRESSION FOR A HPGe DETECTOR Si-PSD SPECTRUM (POSITION vs. ENERGY) MEASURED AND CALCULATED PRODUCTION CROSS SECTION FOR Te NUCLEI SPLIT ANODE GAS IONIZATION DETECTOR FOR DARESBURY RMS SEPARATED GAMMA SPECTRA FOR MASS

11 FIGURE 3.10 SCHEMATIC DRAWING OF THE YALE NEUTRON BALL DETECTOR DRAWING OF AN INDIVIDUAL NEUTRON DETECTOR ELEMENT TIME OF FLIGHT AND PULSE SHAPE RESPONSE OF A NEUTRON DETECTOR FIGURE 4.1 GAMMA-GAMMA SPECTRA FOR SEVERAL GAMMA RAY ENERGIES GAMMA RAY SPECTRA GATED ON ONE AND TWO NEUTRONS COMPARISON OF RECOIL MASS SPECTROMETER AND NEUTRON BALL SPECTRA ANGULAR DISTRIBUTION OF kev AND kev GAMMA RAYS LEVEL SPECTRUM FOR 114Xe MIXING PARAMETER FOR THE kev TRANSITION... 77

12 I. INTRODUCTION Recent experimental studies have documented the existence of broken reflection symmetry in the low lying excitation spectra of light actinide and lanthanide nuclei, manifested by rotational bands of alternating parity and odd-even spins. These rotational bands include states of spin and parity J n =..., 4+, 5%6+, 7%... and decay with enhanced electric dipole (El) transitions. These El decays appear to arise from a nonzero dipole moment in the intrinsic state of the nucleus. Such a static nonzero intrinsic dipole moment implies a polarization of the nucleus. Normally, the nuclear charge distribution is symmetric implying that the ground state intrinsic dipole moment is zero, and to first order, a dipole operator, at low excitation energy, is interpreted as a translation of the nuclear system. Non spurious dipole excitations in nuclei usually occur at relatively high energies in the form of the well known giant dipole resonance (GDR). The GDR is a dynamic excitation, induced by an external electromagnetic field, in which the proton and neutron fluids oscillate out of phase. It requires from about 10 to 25 MeV excitation energy and exhausts about % of the quantum mechanical El sum rule [Go48, Le50, St50, Be75, My77, Bo81, Bo81a, Be82]: Sl(El) = X(Ef -Ej) B(E1: i -> f) f (1.1) i 9 e2ft2nz...n Z... s 4 ^! S ' X = 210X ( M e V -m b > where i (f) stands for the initial (final) state, Ej (Ef) is the corresponding energy, B(E1) is the reduced nuclear transition matrix element for electric dipole (El) transitions, m is the free nucleon mass, N is the neutron number, Z is the proton number, and A is the total number of nucleons. It follows then that polarization of the nucleus at low excitation energy or in the ground state implies a static intrinsic dipole moment and 1

13 (side view) (end view) 0 Spherical Quadrupole Deformed Prolate D (side view) (top view) QctUPQlg Deformed Quadrupole Deformed Oblate Figure 1.1 Various Nuclear Multipole Shape Deformations 2 thus broken reflection symmetry. Such reflection asymmetric states represent a new venue for nuclear structure models, and more recently were considered by Iachello [Ia89, Ia89a] in hadronic structure. In general, nuclei may have a nonspherical shape and their low energy spectra are well understood by including only the spherically symmetric and quadrupole terms in the multipole expansion of the nuclear shape, thereby leading to a quadrupole deformed potential. The quadrupole deformation may be oblate or prolate; in either case, however, there is a natural symmetiy axis of the nuclear shape (see Fig. 1.1). Reflection symmetry implies that the nucleus is symmetric under rotation of 180 about all axes through the body center which are perpendicular to this symmetry axis. However, an intrinsic static dipole moment is asymmetric under this operation and thus breaks this symmetry. Currently, there are two postulated mechanisms which break reflection symmetry and ultimately lead to static dipole moments in nuclei. One of these is based on (and constitutes an extension of) the discovery of "nuclear molecules" by Bromley et al. in the 24Mg system (12C + 12C) [Br 60]. Further study of clustering

14 in nuclei has shown that such a dinuclear configuration which is not composed of identical particles breaks reflection symmetry. For example, in the alpha cluster model, the dinuclear configuration is described by the separation vector between the center of mass of the alpha particle cluster(4he nucleus) and the rest of the nucleus, leading to a vector degree of freedom in the nucleus. This model was first proposed by Iachello in 1981 [Ia81]. Energy levels and transition strengths in this model are calculated using spectrum generating algebras, and associated dynamic symmetries, based on the compact Lie group U(4). The second mechanism is the inclusion in the nuclear shape expansion of odd pole deformations. The lowest nonzero odd pole included is the octupole term (X = 3). This term leads to a nonzero dipole moment through the redistribution of charge along the nuclear surface by the classical repulsion of charge to the sharp edge of an octupole deformed nucleus [St56, St57]. This effect is the basis of the static octupole deformation model. In this model one employs a deformed potential energy surface to reorder the standard shell model nuclear orbitals. In this deformed shell model, the potential is then inserted into the Schrodinger equation to calculate observables of the problem in the usual way [St56, St57, Bo59]. A dipole degree of freedom in the molecular nuclear system has several direct, observables [Ia81]. If the nuclear molecular configuration is reflection symmetric (for example, the two nuclei are identical as in 12C + 12C), a band including only positive parity states (corresponding to rotational excitation) should be built upon intrinsic molecular states. These rotational bands are quadrupole bands connected by enhanced electric quadrupole gamma ray transitions. The predicted enhancement above single particle transitions is of roughly the same order (100 times single particle strength) as for a quadrupole shape deformed nucleus with no molecular configuration. The distinguishing feature of the spectrum occurs when the configuration is reflection asymmetric; the cluster nuclei are not identical. The nucleus is no longer symmetric with respect to reflection through a plane perpendicular to the symmetry axis. Thus, 3

15 states of both even and odd spins are allowed in the K=0 band (where K is the projection of the angular momentum in the body fixed system). However, reflection through a plane containing the symmetry axis is still a symmetry operation and the normal connection between spin and parity is unchanged [P=(-)J] [Bo75]. In this case, the rotational band will contain an alternating parity sequence of states 0+, T, 2+, 3, 4+, 5->... A second signature of broken reflection symmetry is the existence of enhanced, intraband electric dipole (El) gamma ray transitions. These transitions can occur when the two constituents of a molecular configuration have different Z/A ratios, leading to a separation between the center of charge and the center of mass of the composite nucleus [Ia81]. This separation gives a nonzero intrinsic dipole moment and thus leads to enhancement of the El transitions. Although the El gamma ray transitions are enhanced by several orders of magnitude with respect to the average strength of Els in nuclei, the enhanced transition strength is still a small fraction of the single particle transition strength as given by Weisskopf [We51J. If the composite nucleus shows a molecular configuration composed of distinct clusters with equal Z/A ratios, as in the case of l2c, the intrinsic dipole moment vanishes and the El transitions are forbidden in first order by isospin selection rules [Ra52, Tr52, Ge53j. A quantitative measure of the expected El enhancement has been derived by Alhassid, Gai, and Bertsch [A182] in the form of a new "molecular" quantum mechanical sum rule for El transitions. In this sum rule, the contributions due to excitation of the cluster particles in a two body molecular configuration are removed and only excitation of the molecular configuration is included giving the expression: 4 cm,.^atl 9 (N-Z)21?e2 Si(El,a + A2) - 4j[ A(A_4) 2m d'2)

16 for the specific case of an alpha particle cluster. In heavy nuclei, A >> 10, this expression leads to a reduced El transition strength of the form B(E1) oc (N-Z)2 / A2 and an explicit global dependence of the expected El strength in nuclei on isospin and mass. This Ph.D. dissertation is motivated by this specific prediction and is designed to test the explicit isospin dependence of enhanced El transitions in nuclei, as discussed below. In this work, we attempt to test the alpha cluster model and the octupole deformation model by checking the predictions of the models in a new region, near the N=Z=50 closed shells in the nucleus 114Xe, where the ground state nuclear isospin, Tz=(N-Z)/2 = 3, differs by roughly an order of magnitude from that in the previously studied actinide and lanthanide regions. Measurement of the low-lying structure of this nucleus (through gamma ray spectroscopic methods) further tests the global existence of reflection asymmetry, and specifically tests the isospin dependence predicted in the alpha cluster model. Additionally, the two models predict broken reflection symmetry in different nuclei in this region. Octupole deformation calculations [Sk90] show large low lying deformations in or near N=Z nuclei in this region, however, the alpha cluster model explicitly predicts decreased B(El)s as one approaches N=Z nuclei. Indeed this study provides the first evidence for broken reflection symmetry near the N=Z line. Although we have measured only two B(El)s in this nucleus, the structure of the level spectrum and the strength of one of them (larger by more than an order of magnitude than reflection symmetric models of nuclear structure can account) require the introduction of broken reflection symmetry. One can see that measurement of broken reflection symmetry effects in this region provides a crucial test of the theoretical models. The low-lying spectrum of excited states characteristic of broken reflection symmetiy as described in the alpha cluster model can be calculated, in principle, by constructing a molecular nuclear potential and inserting it in the Schrodinger equation. 5

17 However, this approach is fairly complicated, especially when the coupling to other degrees of freedom in the nucleus becomes important. An alternative approach suggested by Iachello [Ia82, Ia82a, Ia83, Da83], which has been successful in reproducing the spectra of reflection asymmetric configurations, is the use of dynamic symmetries of the compact unitary Lie group of dimension 4 (U(4)) to create a Spectrum Generating Algebra (SGA) [Ia81], or the vibron model. The SGA based on U(4) contains two possible complete chains of subgroups which contain the group 0(3): (I) U(4) 3 0(4) 3 0(3) 3 0(2) (1.3) (II) U(4) 3 U(3) 3 0(3) 3 0(2) The subgroup 0(3) is the physical rotation group and must be contained in the chain, if angular momentum is to be a good quantum number. Each chain is associated with a dynamic symmetry of the Hamiltonian of the system. The first chain (I), the 0(4) subchain, generates a low lying spectrum of rotational bands with states of alternating parities, as discussed above, built upon molecular vibrational states. The second chain (II), the U(3) subchain, produces dipole vibrational bands also comprised of sequences of states of alternating parity. Physically, the 0(4) subchain corresponds to a rigid molecular configuration and the U(3) subchain to a soft molecular configuration dominated by dipole phonon vibrations. In both these chains, corresponding to the dynamical symmetries mentioned above, the nuclear excitation is predicted to decay via enhanced El and E2 gamma ray transitions. A first order treatment of the full nuclear system must also include the collective degrees of freedom of the nucleus which are well known and are described by the model known as the Interacting Boson Approximation (IBA) using the group structure U(6). This coupled model, the hybrid vibron model, was outlined by Iachello 6

18 and Jackson [Ia82] and later applied by Daley and Gai [Da84] and uses the coupled group structure U(6) U(4) to determine the nuclear excitation spectrum. The use of the group U(4) in generating spectra is based on the importance of a vector degree of freedom for the description of the molecular state [Ia81, Ia81a, Ia82, Ia82a]. While nuclei provide a very diverse medium to study the various aspects of this model, the phenomenon of reflection asymmetry is not exclusive to nuclei. In fact, any quantum mechanical system containing one or more independent vector degrees of freedom may be described in this group theoretical expression of reflection asymmetry. For example, diatomic molecules exhibit a vector degree of freedom characterized by the separation vector between the center of the two atoms, and the vibrational spectra of these molecules is well described by the SGA method using a U(4) symmetry [Ia81a]. Indeed, triatomic molecules involving three objects have been described using a coupled approach (see Chapter II.2 p. 28 and Figure 2.4), where the system is represented by two independent vector degrees of freedom and the group symmetry is then U(4) U(4) [Va82]. Extending this description to the realm of particle physics, mesons and baryons can also be represented by di- and trimolecular configurations of quarks, and one may be able to calculate their excited spectra using the SGA approach in an analogous manner to that described above for nuclei and molecules. Iachello [Ia89, Ia89a] has recently demonstrated that the excited spectra of hadrons is well reproduced by such an approach, indicating that bound quark pairs may indeed be represented by a vector degree of freedom as oscillating "molecular strings". In this case, the relative motion of quark pairs is represented in the SGA model by their separation vector and, indeed, one can see in a simple geometric picture that the structure of the quark-antiquark pairs in mesons breaks reflection symmetry (see Figure 1.2(a)). For hadronic structure, Iachello suggests further that one needs to couple the internal flavor and spin degrees of freedom, characterized by the SU(6) «SU(3)flavor 7

19 SU(2)spjn representation, to the relative (collective and geometrical) motion of the quarks, characterized by the separation vector and thus the group structure U(4), giving the coupled structures SU(6) U(4) for mesons and SU(6) U(4) U(4) for baryons respectively [Ia89, Ia89a], In the case of mesons, this coupling has the effect of adding three additional terms to the Giirsey-Radicati mass formula [Gu64] of the form e^co(ffl+2)+l +f*vjl(l+l)+4 + g'\jj(j+l)+ 5 (see Ch. II eqn. II.2.12). These terms describe radial excitations ( ), Regge trajectories (different L values), and spin-orbit couplings (J = L+S).The total spin J of the (resonant) state is determined by the L-S coupling of the intrinsic spin of the state and the rotational angular momentum. In the case of mesons, the meson spin (given by the two quarks of spin 1/2) can be either 0 or 1. For spin zero mesons the (resonance) spin is just given by L, however, for spin one mesons we have a multiplet of spins: L, L+l, or L-l. If the spin-orbit coupling is small, the mass of all three resonances in the multiplet should be nearly the same. This is consistent with the experimental data as evidenced by the horizontal lines in the spectrum (see Figure 1.2(b)). For baryons, which are composed of three quarks, the total spin is either 1/2 or 3/2 depending on the quark spin alignment. As in mesons, the spin orbit coupling is relatively small. The quark configuration of baryons is more complicated than in mesons, however. Catto and Giirsey [Ca85] have suggested that at low spin (J<9/2), the quarks are arranged in a trilocal configuration and the baiyons behave as nonlinear strings. Iachello has suggested [Ia89, Ia89a] that such a configuration leads to parity doubling of the resonant states. For example, the 3/2+ Pj3(1720) N*-resonance is nearly degenerate with the 3/2* Di3(1700) resonance [He90]. No parity doubling can occur for the K=0 resonances. For resonances of higher spin, the parity doubling gradually disappears as the quarks reorient in a bilocal configuration (see Figure 1.3(a)), and the resonant spectrum contains radial excitations, and Regge trajectories similar to the meson resonance spectrum [Ia89, Ia89a]. 8

20 9 (b) (a) q o % L ^. oq q c=oq ~o=> (c) Figure 1.2 (a) Quark structure of mesons, (b) Calculated spectra of mesons with S=1 and S=0, (c)observed spectra of mesons with 1=1 (Isovector) and 1=0 (Isoscalar), taken from Iachello [Ia89, Ia89a].

21 In mesons, the Regge trajectories, built on radial excitations, have the same characteristic pattern of alternating parity and odd even spins as do the excitation spectra of nuclei exhibiting broken reflection symmetry (see Figure 1.2(b)). The baiyons have a three quark structure whose solution is more complicated, requiring a coupled algebra for calculation of the relative motion alone and we refer the reader to 10 (a) M* (G«V*) (b) I 1/2 3/2 5/2 7/2 9/2 11/2 13/2 15/2 J 1/2 3/2 V2 7/2 9/2 11/2 13/2 15/2 J Figure 1.3 (a) Possible quark structure of baryons (b) Experimental spectra of N* (1=1/2) and A* (1=3/2) excited baryons. The occurrence of parity doublets at low spins is clear. Taken from Iachello [Ia89, Ia89a].

22 the paper by Iachello [Ia89, Ia89a] for details of the baryonic spectra (see Figure 1.3). It appears that broken reflection symmetry is a ubiquitous phenomenon and not unique to nuclear structure physics. Nuclei, however, provide a very rich area to study the consequences of broken reflection symmetiy and to develop and test theoretical models incorporating broken reflection symmetiy as applied to atomic molecular physics, nuclear molecular physics and hadron molecular physics. Several nuclei exhibit low lying spectra characteristic of broken reflection symmetry, including some of the light actinides (218Ra, 220Ra, 22^Th, 222Th, 224Th) and 180 [Fe82, It82, Bo83, Ga83, Ga83a, Ru83, Wa83, Co84, En84, Bo85, Sh85, Ga89, Ga91]. The light actinides especially show characteristic signatures of broken reflection symmetiy, such as enhanced El and E2 gamma ray transitions within a band of alternating parity states built upon the ground state. In 218Ra [Fe82, It82, Ga83a, En84], for example, measured reduced El matrix elements (B(E1)) as large as 6 x 10'3 Weisskopf units (W.u.) have been measured [Ga87], an enhancement of two orders of magnitude over the typical B(E1) strength. The signature of reflection asymmetry in these heavy nuclei is very clear. In the nucleus 180, coexistence of two degrees of freedom, including single particle excitations and collective quadrupole rotations were suggested [Fe65, Br66, Ar67], A group of states of alternating parity built on the 4p-2h 02+ state at 3.63 MeV has been suggested as a signature of broken reflection symmetiy in 180 [Ga83a, Ga89, Ga91], extending the coexistence model to also include collective molecular dipole excitations. More recently, studies concentrated in the Ba-Sm region near mass 150 have unveiled alternating parity bands, suggestive of reflection asymmetry, in the nuclei 148,146jqd, 146Ce, and 144Ba [Ph86, Ph88, Ur88]. These bands are characterized by El transitions with extracted (but not directly measured) B(E1) transition strengths of «3 x 10 3 W.u. The data show a signature in the ground state bands of these nuclei. It is interesting to note that all of these nuclei occur near and slightly above doubly magic 11

23 nuclei (i.e. nuclei in which the proton and neutron shells are both closed). Indeed, in the shell model, octupole deformations are predicted to occur where orbitals differing by Al=3 appear near the Fermi surface: N or Z = 34, 56, 88 and 134, just above the closed shells at N or Z = (28), 50, 82 and 128. As one moves further away from shell closure, quadrupole rotations dominate the spectrum and reflection asymmetry occurs at relatively higher energies. Consequently, just above double shell closure is where we expect to be able to observe most clearly the effects of broken reflection symmetry. In this work we address the question of global mass dependence and isospin dependence of enhanced El decays in nuclei. Both the static octupole deformation model and the alpha cluster model make global predictions concerning the relative enhancement of electric dipole and quadrupole transitions arising from broken reflection symmetry. In the static octupole deformation model, the nucleus acquires a nonzero dipole moment through polarization of the nucleus. The nuclear shape deformation polarizes the nucleus through a redistribution of charge, reflecting the (classical) effect of large electric fields near surfaces with small radius of curvature. Thus, the center of charge in an octupole shape is displaced from the center of mass. The total intrinsic dipole moment is given by three terms as: D0 = (1.4) where the Liquid Drop term (D^) is given by the proton fluid, the n-skin term (D+s/an) by tbe neutron fluid, and the third (shell model) term ( Dq ^) is given by a microscopic sum over individual nucleons in the deformed independent particle model [Le85]. Calculation of the first term only, based on octupole deformation in a one fluid liquid drop model predicts an intrinsic dipole moment due to the redistribution effect given by: D0 = 6.9 x 10"4 AZ j82 e-fm (L5) [St56, St57, Bo59], where and 3 are the quadrupole and octupole shape deformation parameters. Calculations by Leander [Le85] suggest that the neutron 12

24 fluid in the two fluid liquid drop model also has a significant contribution to the dipole moment, but with opposite sign. This neutron skin term turns out to be of the same order of magnitude as the redistribution term, greatly reducing the dipole moment as given by Strutinsky. In detail, the liquid drop and neutron skin terms in the two fluid model are given to first order by [D086]: 13 D 'o = C,M Z D 'ff** = * 0, e2- Tl 6L. 15., _ 15 NZ.. _ * U + JKI + 8QA'VJ ; ^ - 2 x ^ 3 5 a M * (1.6) where N-Z I+(9^/80 rp Q) ZA-2/3 - A 1+(9J/4Q) A-l/3 U-Y) Here J is a volume symmetry-energy coefficient [St56,Bo59], Q is the stiffness of the neutron skin, K is the nuclear compressibility coefficient, and L is the density symmetry coefficient [Bu91]. The expression for the shell model term [St67, St68, Br72, Bo72] is given by D ^ - * f < z n > * * - fl-8) The total expression for the dipole moment in this model has quite a complicated dependence on the proton number Z and mass A of the nucleus and a simple global trend is not apparent from the equations. It turns out that the effect becomes important near and above doubly closed shell nuclei, as observed experimentally. In order to study global trends in a first order approximation, we can scale the effect by A Z, as given by the liquid drop term of the dipole moment [St57, D086]. One must add the caveat that predictions concerning a specific nucleus, as opposed to general trends, should be based on a complete calculation and not solely on comparison to the systematic predictions.

25 In the alpha cluster model the situation is much simplified, the nuclear dipole moment is due to a nuclear molecular configuration consisting of a core nucleus peripherally bound to an alpha particle and the observed structure is due to excitation (vibrations and rotations) of this configuration. The deformation is caused by collective effects of a few valence nucleons rather than realignment of the entire core nucleus as in the octupole deformation model. Then, if the core nucleus (the nucleus less the alpha cluster) is not self-conjugate (N * Z), the charge to mass ratio of the core and the alpha cluster are different, leading to a separation of center of charge and center of mass. This gives a dipole moment of [A182] D = 2(N-Z)/A ed0> (1.9) where dg is the separation distance between the centers of the two clusters. Hence, in the cluster model one predicts a global [(N-Z)/A]2 dependence of enhanced Els. One would also expect that such a nucleus would be characterized by a large alpha reduced width and this is indeed the case. The compiled data of ground state reduced widths for alpha particle decay show systematically large reduced widths near and above shell closure for nuclei (see Figure 1.4). Experimentally, this is where nuclei exhibiting characteristics of broken reflection symmetry occur. However, the measured enhancement of the El transition strength in these nuclei is approximately constant in the nuclei studied to date (see Table 1.0). This is consistent with the global (N-Z)/A dependence on isospin and mass predicted by the cluster model. For all nuclei studied thus far, (N -Z)/A is relatively constant. As a comment in passing we remark that the data of Table 1.1 do not show an explicit dependence on (A-Z)2 as would be predicted in the liquid drop model assuming similar deformations. In this model the difference between theoretical prediction and the data may be reconciled by introducing a shell correction term such as in equation 14

26 Figure 1.4 Reduced alpha particle decay widths in nuclei normalized to 212Po. (1.8). This term reduces the difference in predicted strength between the actinide region and the Barium region. In order to test the global model predictions of enhanced El transition strength in reflection asymmetric nuclei, a search for reflection asymmetry in the region above the doubly magic nucleus 100Sn was undertaken. As can be seen from Table 1.0, in this region nuclei with a value of the isospin parameter (N-Z)/A much smaller than in previous studies are accessible, allowing for a test of this predicted isospin dependence of enhanced Els. The El enhancement in this region, however, is expected to be smaller by an order of magnitude than observed in the actinide and lanthanide regions. Since nuclei in this region must be nearly self conjugate, the separation between the center of charge and the center of mass must be small, leading to a small intrinsic dipole moment. The El transitions in nuclei in this region should still be enhanced by

27 16 Table 1.1 Nucleus B(E1)/B(E2)* (N-Z)2/A2 B(E1)/B(E2) (N-Z)2/ A 2 (AZ)2 (l(r7 fm*2) (x nr2) (HT5 fm*2) (x Xe Th Th <>rh Ra Ra Nd Nd Ce Ba* * Experimental ratio of reduced transition strengths B(E1)/B(E2) in nuclei showing broken reflection symmetry, tabulated as a function of AZ and (N-Z)/A, the global dependences predicted in the liquid drop octupole model and alpha cluster model respectively. B(E1)/B(E2) is taken as the average value in the nucleus. B(E2) values in these nuclei are quite similar (between 40 and 70 W.u.) and the ratio B(E1)/B(E2) represents the El strength. * In this nucleus, there are large fluctuations in B(E1)/B(E2). Surprisingly, the ("forbidden") El transition from positive parity states are an order of magnitude larger than the ("allowed") ones from negative parity states. The last El transitions, i.e. at low spins, drive the average to a low value for this nucleus.

28 17 approximately an order of magnitude above the measured average B(El)s in nuclei. We have thus undertaken a study of ll4xe in search for isospin dependence of enhanced E l transitions in nuclei exhibiting broken reflection symmetry. Theoretical calculations in the octupole model show potential minima at nonzero octupole deformation in the neutron deficient ^Ba and 54Xe isotopes with N = Z near A=112 [Sk90]. However, E l transitions are forbidden in first order in selfconjugate nuclei and a search must be performed with nuclei having N >Z. However, the calculations of Skalski [Sk90] show a decrease in the octupole deformation as N-Z increases. Indeed, the level spectrum of 116Xe (see Figure 3.1) shows that the quadrupole effects are dominant at low excitation energy in this nucleus. Consequently, a gamma ray spectroscopic study of the nucleus 114Xe (N -Z=6) was undertaken. We report here on two experiments on ll4xe, one utilizing the Recoil Mass Separator (RMS) at Daresbury National Laboratory [Ru87, Ru88] and a second using the 2x Neutron Ball at Yale University. In both experiments the nucleus was produced through the fusion evaporation reaction 60Ni(58Ni,2p2n)114Xe at Ej_=243 MeV with a production cross-section of the order of lmb. A search for the characteristic signature of broken reflection symmetry was performed using gamma spectroscopy to study characteristics o f emitted gamma radiation. The only previous measurement of the nucleus 114Xe was a 0 decay study in which the first 2+ state was identified and the first 4+ state was also tentatively assigned [Ro80]. In this study, the low lying level spectrum was extended and three transitions were determined to be of El character with the reduced transition strengths extracted for two o f these transitions. In Chapter II we give a brief summary of the theoretical basis of broken reflection symmetry including a brief overview of spectrum generating algebras and the standard and deformed shell model. Experimental considerations and techniques are discussed in chapter III and results of the measurement are presented in chapter IV and interpreted in terms of the theoretical models in the discussion in chapter V.

29 II. T H E O R Y O F B R O K E N R E F L E C T I O N S Y M M E T R Y II.l. Alpha Particle Cluster Model The alpha particle cluster model of nuclei is based on the existence of subnuclear clustering within nuclei. Cluster structure in the unbound nuclear system leads to resonances in the scattering cross section. The formation of cluster states in bound states of nuclei is energetically unfavorable except in certain cases. The formation of alpha particle clusters (4He) within the nucleus is one such case. The energy required to separate two protons and two neutrons from the nucleus is offset by the large binding energy of 4He. This large binding energy is a direct result of the nuclear shell model in which the lowest shell, lsy2, is filled by 2 identical nucleons. Thus 4He is the lowest mass nucleus in which both the neutron and proton shells are filled. For nuclei which contain several (more than two) neutrons and protons more than the nearest closed shell, the formation of an alpha cluster among the valence nucleons gives the nucleus a two body molecular configuration (see Figure 2.1). The core nucleus is a very tightly bound spherical nucleus as is the alpha cluster. It requires a relatively large excitation to promote a nucleon from within either closed shell cluster, on the order of a few MeV. The low lying excitation can come only from excitation of the few valence nucleons not bound in either cluster or from excitation of the molecular configuration itself. This excitation includes vibration and rotation of the dinuclear configuration. This configuration is described by the separation vector between the centers of the two nuclei leading to a dipole degree of freedom. The magnitude of this separation vector is taken to be the sum of the radii of the two constituent nuclei, Rj + R2, where the radius is parameterized by the formula R =R qa 1/3 (R0=1.2fm). In this picture, the nucleus consists of two contiguous spheres. 18

30 19 A \ z Figure 2.1 Geometric representation of alpha clustering in nuclei and classical variables. ft ^4 ^ ^ ^ The dipole operator can then be decomposed [A182] as D = Dj + D2 + Dj^ where Dj (i= 1,2) is the dipole operator of the /th cluster (Dj = e Z(?j,p-Rj,CM)) and is the P "molecular" dipole operator. The molecular dipole operator can be constructed simply by calculating the separation of the center of charge from the center of mass of the composite nucleus assuming the clusters are spherical distributions of charge and mass. Given the cluster mass and charge by Aj, Z j and A 2, Z2, A j+ A 2=A and Z j+ Z 2=Z, the center o f charge and center of mass conditions are given by r 1 A 1 + r -j A? r 1 Z 1 + r? Z? CM 1 A j + A2 a 1 = 0 CC = 1J Zx +, Z2 Z L (II.l.l) The center of charge is calculated in the Center of Mass system and defining d0 to be the separation vector between the centers of the spheres, the "molecular" dipole moment becomes:

31 20 -* r z ]a 2iZ2a 1i -> # A do (II.1.2) Assuming cluster one is an alpha particle, we obtain Dj^ = e 2(N-ZV A d Q. The estimate of the transition strength in nuclei is usually given in terms of the expected transition rate if the transition is due to a single particle changing orbits in the shell model. Estimates of the expected single particle transition rate for different multipole transitions (Weisskopf units) have been given by V. Weisskopf [We51]. However, for transitions due to the molecular dipole moment defined above, a more appropriate unit, the "molecular Weisskopf unit" has been suggested by Alhassid, Gai, and Bertsch [A182]. This new estimate of transition strength is determined by replacing the nuclear radius with the separation between center of charge and center of mass (2 d0 (N-Z)/(AZ) ) in the Weisskopf estimate. For example, in mol.w.u. = [(2 d0 (N-Z)/(AZ))/(roA1/3)]2 = 1.8 x 10'3 W.U. This gives a rough first estimate of the transition strength. A more detailed estimate is given in the calculation of a "molecular sum rule." This sum rule, derived by Alhassid, Gai, and Bertsch, is deduced from the normal energy weighted electric dipole sum rule, Sj(El), by subtracting the appropriate sum rules for the cluster nuclei from the sum rule for the composite nucleus. This is reasonable only when excitation of the clusters themselves is not considered. Following this procedure, we derive the molecular sum rule: qrrn 9 h\eft 471 A A j A 2 2 m /T. 9 (N-Z)2 ft2*2 S1(E l;a + A 2) = 47t A (A _4) 2m (II.1.3) The microscopic calculation yields the same result [A182] suggesting that this sum rule is model independent. Using this scale, Alhassid, Gai, and Bertsch have shown that enhanced Els in 180, for example, are clearly collective in terms of a molecular

32 21 excitation, exhausting up to 13% of this sum rule and corresponding to as much as 15 mol.w.u. In this model, the spectrum of the nucleus is determined completely by the excitation of this dipole degree of freedom. It has been shown [Di80] that a vector degree of freedom, in this case the separation vector between the two clusters, can be described using group theoretical techniques by the compact group U(4). Since a vector is described by three classical variables, it was shown [Di80] that the corresponding SGA Hamiltonian acquires U (3+l) symmetry. Practically, the nuclear spectrum is not a pure configuration and mixing with the normal collective quadrupole rotational excitations occurs. This mixing is incorporated in a hybrid model which couples the quadrupole U(6) symmetry [Ar75] with the dipole collective U(4) tymmetry, leading to the Hybrid Cluster Model used by Daley and Gai [Da84]. These models make use of the dynamic symmetries of the corresponding groups to produce a spectrum generating algebra which is then used for calculation of all observables. II.2. Spectrum Generating Algebra Group theoretical methods provide a convenient method of constructing rotation-vibration spectra. A full solution of the Schrodinger equation for a complex system is often difficult or impossible, especially if the potential is not well known. A complete expression of the wavefunction is necessary in order to calculate the matrix elements of the operators of interest. The potential can be parameterized and fit to experimental energy levels or to a theoretically calculated potential, if one exists. Calculation of matrix elements involves complex integration and differentiation. A simpler approach, using algebraic techniques, is possible through the use of group theory. Instead of assuming a model potential and solving the resultant Schrodinger equation to calculate the spectrum, the existence of a dynamical symmetry is assumed.

33 22 The simplest method to reproduce rotation-vibration spectra is achieved through the use of creation and annihilation operators in second quantization. Because of the strong pairing force between identical particles in nuclei, it is appropriate to consider bosons as the basic building blocks of the theory [Ar75]. The creation (ba) and annihilation operators (b*) are assumed to satisfy Bose commutation relations: P>.b/] = 8aa'. [b.v]=0, (b/b/l = 0. (II.2.1) These bosonic operators are chosen to represent the degrees of freedom of the system to be studied. All the quantum mechanical operators are written as expansions in bilinear products of the creation and annihilation operators and have the symmetry of the unitary group U(n) generated by these operators. In order to construct Hermitian operators, the annihilation operators b ^ (A. = 1,2; p= -X,-X+1,...X) must be replaced with Hermitian operators defined by b ^ = (-1)*-+m bx,_h. The Hamiltonian, for example, may be written as H = h0 + ( Saa. b ; b.. ) + I ( -'» b ; b. b b, ) + aa' aa'pp' where hq, 0^, u ^ p -,... are free parameters. The bilinear products (II.2.2) b*ba>form the generators of the unitary group U(n) where there are n creation and n annihilation operators giving n2 generators. The Hamiltonian then becomes H = h0 + 2 > _. G _.) + i G. G ((.) + (II.2.3) aa' aa'pp' where the n-generator term in the expansion is called the n-body part of the expression. All calculations are reduced to algebraic manipulation of the generators and the creation and annihilation operators. simplifies some complex calculations. The method of spectrum generating algebras However, since it is based on compact Lie groups, U(n), whose representations are discrete and finite, its application is generally limited to bound state spectroscopy. The study of continuum states (unbound

34 23 scattering states) may be described by generalizing the group theoretical representation to include non-compact groups such as U(n-l,l). This problem is currently under study. The use of spectrum generating algebras (SGA) to study dynamic symmetries in nuclear structure was introduced and applied to the low lying excitation spectra of medium mass nuclei [Ar75]. This model, called the Interacting Boson Approximation (IBA) model, is based on the premise that the dominant factors in low energy excitations are the pairing forces between like nuclei and the quadrupole-quadrupole interaction between non-identical nucleons. The first effect leads to the use of boson operators in the theory and the second effect defines the dimension of the problem. It has been shown [Di80] that the dimension n of the group appropriate to the problem is related to the number of degrees of freedom r in the classical limit: n = r+ l. In the IBA, the classical quadrupole shape is defined by five variables: three Euler angles 0, <t>, and vy, and two shape parameters (3 and y. The appropriate group is therefore U(6). The six boson operators defined include one scalar a boson (J7t=0+, denoted o +,a) and five quadrupole d bosons (J7t= 2+, denoted d*, d^ p=-2,-l,0,l,2). The generators of the algebra are the 36 bilinear products of these operators. The IBA model is then obtained by writing the operators as a product of these 36 generators as in eqn. II.2.3. Because the operators must obey Bose statistics, they are then diagonalized in the totally symmetric representation of U(6). In the IBA, these operators are considered to be quanta representing quadrupole surface excitations (quadrupole phonons). In the case that the system of interest can be described classically as a two body molecular configuration, the system is characterized by the separation vector connecting the centers of the two constituents. This vector is fully characterized by three classical variables (for instance r, 0, and <J>, see Figure 2.1). Hence, in the SGA approach, the rotational and vibrational excitations of the separation vector (dipole deformation) are described by a Hamiltonian acquiring a U(4) dynamic symmetry,

35 24 generated by four bosonic creation and annihilation operators, the "Vibron" model, with one scalar operator denoted o +,o (Jn= 0 +) and a vector consisting of three operators denoted (J7r= l, p = -1,0,1). The bilinear products of these four boson operators form the 16 generators of the group U(4) [Ia81, Ia82, Ia83], The Hamiltonian of this system may be written as an expansion in the group generators as in eqn. II.2.2. It is usually more convenient to write the expansion in terms of the tensor products of the boson operators [ ]«=, ( A. X' x x* kp) bx^ bxy (II.2.4) r n i where b ^ represents any of the creation operators and k and p are the angular momentum coupling and projection respectively. For example, [ 7t+ x n+ ]2 = S <1 p 1 p' 2 p) ttv. (112.5) The tensor product is a sum over bilinear products weighted by the appropriate Clebsch-Gordan coefficient. In the expansion in tensor products, the expansion coefficients are linear combinations of the expansion coefficients from the sum over bilinear products. Since the Hamiltonian must be a scalar quantity, terms such as eqn.ii.2.5 which couple to nonzero angular momentum do not survive in the expansion. In order to determine the energy levels, the total number of boson quanta (vibrons) N must be specified. Then the Hamiltonian is diagonalized in the totally symmetric representations of U(4) characterized by N. The number of vibrons, N, is a parameter of the theory and is conserved. In order to calculate the values of other observables, such as electromagnetic transition rates, the same method is employed. For example, the transition rates of electric dipole radiation is calculated by expanding the dipole operator in tensor products coupled to angular momentum one. This operator is then evaluated between the initial and final states which are obtained from diagonalization of the Hamiltonian, tgi = ( V f I D vj/j). These states are written schematically in terms of the number of scalar (nq) and number of vector bosons (nn) as vp) =