Chapter 6. Summary and Conclusions

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1 Chapter 6 Summary and Conclusions The basic aim of the present thesis was to understand the interplay between single particle and collective degrees of freedom and underlying nuclear phenomenon in mass 70 region through spectroscopic investigations. Since the nuclei in this region are transitional in nature, shows wide variety of nuclear phenomenon with increasing proton and neutron number, as well as with spin and excitation energy. Several nuclei in this mass region, with nucleon number close to mid-shell, have been reported to have the collective and noncollective states with moderate deformations related to the competition between different nuclear shapes such as prolate/oblate and triaxial. For example, the structure of Arsenic isotopes changing with increasing neutron number from N = 34( 67 As) to N = 38( 71 As). The shape changing from oblate in 67 As to prolate in 71 As. Whereas similar kind of structural changes have also been observed in lighter Germanium isotopes. The features outlined above, provided a motivation to study the structure of 73 As and 70 Ge. Within the frame work of the present thesis, high spin states in 73 As and 70 Ge have been investigated. Excited states in 73 As and 70 Ge were populated using the heavyion fusion-evaporation reaction 64 Ni( 12 C, p2n) 73 As and 64 Ni( 12 C, α2n) 70 Ge at beam energy of 55 MeV and beam current of 1 pna was provided by 15UD/16MV Pelletron accelerator at the Inter University Accelerator Center (IUAC), New Delhi. The target used was isotopically enriched 64 Ni had thickness 1.5 mg/cm 2 on gold(au) backing having thickness 7 mg/cm 2. Gamma-ray coincidences were measured using the Gamma Detector Array (GDA) developed at IUAC, New Delhi. This facility contains 12 Compton suppressed n-type Hyper Pure Germanium (HPGe) detectors, separated in to three groups 157

2 each consisting of four detectors which are mounted co-axially in Anti-Compton Shields making an angle 45, 99, 153 with respective to the beam direction. The online data has been collected with CAMAC based data acquisition system CANDLE developed at IUAC. The off-line data analysis has been carried out using RADWARE, INGASORT and CANDLE. The experimental investigations also included the study of DCO(Directional Correlation Orientation Ratio). These studies provided information on placement of the γ-transitions and energy levels in the level scheme, spin and parities, γ-ray energies and their relative intensities. The structure of 73 As was limited only to low spin with level spin J π = 25/2 + having an excitation energy 4.1 MeV. These low spin states were interpreted using various theoretical models. In the present work, the energy-level scheme of 73 As has been significantly extended upto spin of J = 37/2 and an excitation energy of 8.7 MeV with the addition of 30 new transitions to the previous work. The previously known low spin structure have also been verified and updated in the present work. A couple of new bands including a J = 1 sequence have been identified and all the earlier reported bands, have been considerably extended up to high spins. The spin assignments for most of the newly reported levels have been made using the observed coincidence relations, R DCO and known spins of low-lying levels. The new experimental results obtained about 73 As are a) extension of 1-quasiparticle positive parity yrast band upto J π = 37/2 +. b) extension of negative parity favored and unfavored sequences upto J π = 37/2 and J π = 31/2 respectively. c) five new weak dipole transitions ( J = 1) which connects the two negative parity sequences. A group of positive parity bands and negative parity bands have been reported along with the other inter band transitions. Spin and parities were assigned to the levels with the help of DCO ratio and from systematics. To understand the microscopic origin of the investigated band structures, theoretical calculations with in the frame work of particle rotor model with a quasi-particle coupled with a triaxially deformed rotor is applied to study the bands observed in 73 As. The calculations obtained for the 1-quasiparticle positive parity yrast band showing large amplitude signature splitting at γ close to 0-20, which in turn supporting the exper- 158

3 imentally observed decoupled nature of J = 2 band. Therefore the PRM calculation suggests that the triaxial deformation for the positive-parity band is more likely prolatelike deformed. Which can be further confirmed by the Cranked Shell Model (CSM) and the Total Routhian Surface (TRS) calculations. The alignment behavior for the positive parity band (labeled as B1) showing smooth variation with rotational frequency having gradual alignment at ω 0.5 MeV. Since, in the odd-proton nuclei in the A 70 region the first proton crossing is blocked, the alignment in yrast positive parity band must be that of a pair of g 9/2 neutrons. Therefore this neutron alignment in 1-quasi particle positive parity band changes the structure in to a 3-quasi particle band. This is also in good agreement with the Nilsson quasi particle crossing frequency calculations, in which the neutron crossing frequency occur at the similar rotational frequency( ω 0.5 MeV) reflecting the experimental results. The PRM calculations for the negative parity band in 73 As suggesting oblate like deformation with γ close to 60 which is in best agreement with experimental energy spectra. The cranked shell model calculations suggesting the first band crossing in negative parity band is due to the pair of g 9/2 neutrons and the expected second band crossing in negative parity band is being due to the alignment of a pair of g 9/2 protons. This configuration assignment is also in good agreement with the Nilsson single particle calculations that the neutron crossing frequency occurred at ω 0.5 MeV and the proton crossing frequency is delayed by more than 0.3 MeV. Therefore this proton crossing frequency supporting the expected second alignment in negative parity band. The shape evolution is further studied with the help of Total Routhian Surface calculations with the Woods-Saxon potential and monopole pairing. These calculations predict that at low rotational frequencies, the nucleus is γ-soft, afterwords at higher rotational frequencies the shape changes in to a collective and non-collective triaxial like prolate corresponds to the configurations in positive and negative parity sequences which perhaps indicating the shape competitions between single particle and collective degrees of freedom. The second nucleus 70 Ge has been populated in the same experiment. In the present investigation, the yrast and near yrast excited levels of 70 Ge have been established up to spin J π = 19 and excitation energy MeV. Multipolarity assignment to the 159

4 observed 1109-keV (dipole nature in previous work) in 70 Ge necessitated crucial change. In present work this transition is assigned as a quadrupole (E2) transition based on DCO ratio which was calculated in three different gates suggesting quadrupole nature to 1109-keV transition. Above this transition a new positive parity structure has been established up to spin J π = 20 + and excitation energy 10.2 MeV and all the earlier reported bands, have been considerably extended up to high spins. The observed band structures have been interpreted in the framework of cranking shell model calculations and the potential energy surface routhians were calculated using Woods-Saxon potential and Ultimate Cranker code. The yrast positive parity ground state band (B1) extended to 14 +, which has been interpreted as due to the alignment of g 9/2 neutron pair. The negative parity structures (labeled as B5) is consistent with octupole vibration at low spins and is crossed by a rotational band with two aligned quasiparticles at high spins. This negative parity sequences (B5) has been extended to 19 was the band based on the πg 9/2 νg9/2 2 configuration. The observation of cascade of quadrupole transitions which constitutes the new positive parity band (B2) signifies the collective behavior in this nucleus at intermediate spins. This band is continuation of the ground state band and becoming yrast at high spins. The experimental alignments and crossing frequencies are confirmed with the Nilsson-single particle routhians calculated at shape parameters β 2 = 0.27, γ -40 with respective to rotational frequency( ω). The predicted neutron crossing frequency ( ω = 0.5 MeV) is in good agreement with the experimental crossing frequency in positive parity bands. The Total Routhian Surfaces and Ultimate Cranker calculations predicted a shape evolution in 70 Ge that at low rotational frequency the nucleus is γ-soft, evolving in to a collective triaxial like prolate with γ -15 having β 0.27 at intermediate spin( ω = 0.5 MeV) and it becomes non collective triaxial like prolate with γ +12 having β 0.27 at higher rotational frequencies ( ω = 0.7 MeV). Therefore the results of the shape calculations depicts that the energy minimum moves towards more positive values of γ with increasing frequency consistent with the loss of collectivity observed in the decay scheme. In brief, the present study obtained substantially new information about the high spin structure of 73 As and 70 Ge. These studies are aimed to explore the possibilities of 160

5 shape coexistence and shape competitions in these nuclei. The results of experimental studies and their comparison with the theoretical calculations have established the shape coexistence of near prolate and oblate shapes in 73 As, which results from the existence of multiple minima in γ deformation with β MeV. In case of 70 Ge, the experimental results not only established the new information on level structure, but also added substantial information on the shape competition between positive and negative parity bands. This shape competition between positive and negative parity bands can be well understand in terms of Total Routhian Surface(TRS) calculations and Potential Energy Surfaces(PES). These studies extend our knowledge about the shape evolution in Arsenic and Germanium isotopes (near mass 70) and the effect of quasi particles on g 9/2 unique parity orbital. In conclusion, the present work established the alignment properties in this mass region to arise from the population of the deformation-driving, unique parity g 9/2 orbital, coupled with the competing influences from the f 5/2 and p 3/2 orbitals that strongly depend on the particle number. The rotationally-based Cranked Shell Model calculations and Particle Rotor Model Calculation were also found to reproduce consistent results in this vibrational-rotational transitional region. In addition, the measurements of the reduced transition probabilities and life times of the observed nuclear states would be an added advantage to confirm the deformations in this region. 161

6 List of Figures 1.1 Nuclear land scape showing different exotic nuclear phenomenon Shows shape coexistence phenomenon studied in various regions of nuclear chart with respect to magic numbers. Figure is taken from Ref. [1] Depicts the piars of orbits close in energy with couplings l = j = 3 susceptible to octupole correlation and the cotupole magic numbers a) Depicts the coupling of angular momentum vectors due to the rotation of current loops of proton particles and neutron holes in Magnetic Rotation. b) represents the coupling of angular momentum vectors in Anti-magnetic Rotation Schematic representation of left handed and right handed chiral system for a triaxial nucleus Nilsson single particle energy levels calculated using Woods-Saxon potential. The levels are labeled with Ω and parity and the energy values are given in units of MeV Variation of BE/A with respect to the mass number of nuclei is shown Showing the variation of different terms in BE equation of liquid drop model with the plot between BE/A and mass number(a) Shell model orbitals with respective to different potential assumed in nuclear shell model Schematic representation of kind of nuclear shapes for different values of deformation parameters like spherical, prolate and oblate shown in order The lund conventions: Schematic of nuclear shapes with respect to the deformation parameters (β, γ)

7 2.6 Schematic of single-particle coupling to core and the Nilsson quantum numbers The partial schematic of Nilsson single particle level diagram is shown Schematic of the body-fixed (intrinsic) coordinates (x 1 x 2 x 3 ) and the laboratory coordinates (xyz) are shown A representative energy spectra of cranking Hamiltonian with Nilsson potential (left), with pairing interactions (middle) and with rotation (right) as a function of rotational frequency ( ω). Spectra was taken from Ref.[16] Total Routhian Surface calculations for the positive parity sequence of 70 Ge at rotational frequencies of 0.5 MeV (left) and 0.7 MeV (right). The contours of equipotential surfaces are separated by 0.20 MeV Experimental routhians (e ) of positive parity ground state band in 73 As as a function of rotational frequency (ω). This band undergoes a crossing around ω c 0.5 MeV Experimental aligned angular momentum (i x ) of positive parity ground state band in 73 As as a function of rotational frequency (ω). The alignment gain is represented as i x Schematic drawing of various kinds of nuclear reaction mechanism possible with light projectiles over heavy nucleus A Schematic of decay of compound nucleus The schematic representation of decay paths of a hot compound nucleus formed in heavy ion fusion reaction Schematic representation of 15UD-Pelletron accelerator at IUAC, New Delhi Absorption cross section for γ-rays in Silicon and Germanium as a function of energy. Plot is taken from Ref.[4] Schematic of Compton scattering phenomenon Schematic diagram of HPGe detector

8 3.8 Representative γ-ray spectrum of 60 Co with and with out Comptonsuppression. Spectrum is taken from Ref.[5] Schematic view of Gamma Detector Array(GDA) Picture of Gamma Detector Array at IUAC, New Delhi Block diagram of electronic circuit used for the Compton suppression system in GDA Block diagram of electronic circuit used for generation of master gate/event Block diagram showing various data-analysis steps followed in constructing final level scheme for nuclei of interest The photo peak efficiency curve for GDA Comparison of energy spectra of detectors 10 and 11 before gain match (top) and after gain match (bottom) Shows typical two dimensional γ - γ matrix Projection of events on an axis of a matrix The total projection spectra without (top) and with background subtraction (bottom) Sample level scheme for illustrating the coincidence relationship Example of gated spectra gated on E1 and E7 with reference to the example level scheme shown in Fig Typical gated spectra on γ transitions 840 kev,1109 kev and 1134 kev of 70 Ge An illustrative level sequence to demonstrate the measurement of intensity Illustration of measuring multipolarities of γ-transitions Intensity distribution for quadrupole and dipole transitions as a function of angle with respect to the beam direction. Figure is taken from Ref.[15] Geometry of detectors arrangement and the directional correlation of two successive γ-rays γ 1 and γ 2 emitted from oriented states Typical angle gated DCO correlation spectra showing the difference between quadrupole and dipole transitions in 70 Ge. The gating transition 1039 kev is quadrupole in nature

9 4.1 The level scheme of 73 As reported in previous work [22] A total projection spectrum of the γ-γ matrix showing transitions belonging to 3nγ( 73 Se), p2nγ( 73 As) and α2nγ( 70 Ge) strong residual nuclei populated in the present experiment Partial level scheme of 73 As established in the present study. The bands are labeled as B1, B2, B3, G4 and G5 for reference in the text γ-ray anisotropy intensity ratio (R DCO ), for a number of J = 2 and J = 1 transitions of 73 As. The quoted errors include errors due to background subtraction, peak fitting and efficiency correction Gated sum γ-γ coincidence spectra of 73 As gated on 609, 912 and 1017 kev of positive parity sequence. Inset portions with expanded vertical scale are drawn to show the weaker high energy transitions. Strong peaks are labeled with energies in kev A representative γ-γ coincidence spectra of 73 As gated on sum of kev (lower panel) of favored negative parity sequence and kev (upper panel) of unfavoured negative parity sequence. Peaks marked with * are contaminants from other reaction channels. Energy values are marked in units of kev The relation between the experimental routhians (e ) with respect to rotational frequency ( ω) for bands B1, B2 and B3 in 73 As The relation between the kinematic Moment of Inertia versus rotational frequency ( ω) for bands B1, B2 and B3 in 73 As The relation between alignment (i x ) and rotational frequency ( ω) (i x - ω graph) for positive yrast bands of odd-a As isotopes 67,69,71,73 As. Here the data for positive-parity yrast band of 73 As correspond to band B1 shown in figure 5.3. Data for other nuclei are taken from Ref. [13, 14, 15] The relation between alignment(i x ) and rotational frequency ( ω) (i x - ω graph) for the negative-parity yrast bands of odd-a nuclei 69,71,73 As. Here the data for negative-parity band of 73 As correspond to the band B2 shown in figure 5.3. Data for other nuclei are taken from Ref.[14, 15]

10 4.11 The plot shows the Cranked shell model calculations for quasi-protons (top) and quasi-neutrons (bottom) of 73 As using shape parameters β 2 = 0.242, β 4 = and γ = -63. The style of lines indicates the parity and signature of the trajectories following the LUND convention. solid lines (+, +) dotted lines (+, -), dot-dashed lines (-, +) and dashed lines (-, -) Total Routhian Surface calculations for the 1-quasiparticle configuration in 73 As at rotational frequencies of 0 MeV (left), 0.55 MeV (middle) and 0.75 MeV (right) for positive parity bands.the contours of equipotential surfaces separated by 0.20 MeV Total Routhian Surface calculations for the 1-quasiparticle configuration in 73 As at rotational frequencies of 0 MeV (left), 0.55 MeV (middle) and 0.75 MeV (right) for negative parity sequences. The contours of equipotential surfaces separated by 0.20 MeV Contour plots of potential energy surface in β-γ plane (0 γ 60 ) for 73 As in constrained triaxial RMF calculations based on PK1 [39] effective interactions. All energies are normalized with respect to the binding energy of the absolute minimum (in MeV). The energy separation between contour lines is 0.2 MeV Rotational spectra for the band with positive parity calculated by PRM for different triaxiality parameter γ are compared with data. In the calculations, the parameters β = 0.35, J 0 = 8 MeV 1 2 and b = 0.1 are adopted The proton single-particle energy levels calculated in Nilsson model. The red line denotes the Fermi surface Rotational spectra for the band with negative parity calculated by PRM for different triaxiality parameter γ are compared with data. In the calculations, the parameters β = 0.2 and J 0 = 8 MeV 1 2 and b = 0.02 are adopted The signature splitting S(I) for the band with the negative parity calculated by PRM for different triaxiality parameter γ are compared with data

11 4.19 B(M1)/B(E2) values for the band with the negative parity calculated by PRM for different triaxiality parameter γ are compared with data A total projection spectrum of the γ-γ matrix showing the transitions belonging to 73 Se(3nγ), 73 As(p2nγ) and 70 Ge(2p4nγ) strong residual nuclei populated in the present experiment γ-ray anisotropy intensity ratio(r DCO ), for a number of J = 2 and J = 1 transitions belonging to 70 Ge. DCO ratios for the transitions ranging from kev are shown in top panel and kev are shown in bottom panel. The quoted errors include the errors due to background subtraction, peak fitting and efficiency correction Partial level scheme of 70 Ge obtained in the present work. The bands are labeled as B1, B2, B3, B4, B5, B6 and B7 for reference in the text A γ-γ coincidence sum spectrum gated on 1039 and 1113 kev transitions in the yrast sequence (band B1) in 70 Ge. Inset portions with expanded vertical scale are drawn to show the weaker high energy transitions. Strong peaks whose energy values are indicated in kev γ-γ coincidence spectra of 70 Ge gated on 840, 1109 and 1134 kev transitions in the newly identified sequence B2. Peaks marked with * are contaminants from other reaction channels. Strong peaks whose energy values are indicated in kev The relation between spin and rotational frequency (J- ω graph) for the positive yrast bands of even-a Ge isotopes 66,68,70 Ge. Here the data for positive parity yrast band of 70 Ge correspond to the band B1 shown in figure 5.3. Data for other nuclei are taken from Ref.[6, 7] The plot showing the experimental routhians (e ) with respect to the rotational frequency( ω) for the bands B1, B2 and B5 of 70 Ge are shown in figure The relations between the alignment and the rotational frequency (i x - ω graph) for the bands B1, B2 and B5 of 70 Ge is shown in figure

12 5.9 Total Routhian Surface calculations for the positive parity states in 70 Ge at a rotational frequency of 0.20 MeV (top), 0.50 MeV (Middle) and 0.70 MeV (bottom). The contours of equipotential surfaces separated by 0.20 MeV The plots shows the potential energy surfaces (PES) calculated using Ultimate Cranker code for the configuration (π, α) = (+, 0) at spin I = 2 (top) and I = 12 (bottom) for 70 Ge The plot shows the potential energy surfaces (PES) calculated using Ultimate Cranker code for the configuration (π, α) = (+, 0) at spin I = 22 for 70 Ge The plots shows the Cranked shell model calculations for quasi-neutrons (top) and quasi-protons (bottom) of 70 Ge using shape parameters β 2 = 0.274, β 4 = and γ =

13 List of Tables 4.1 Transition energy (E γ ), Relative Intensity (I γ ), DCO ratios (R DCO ), Multipolarity of the transition (D/Q) and decay from an initial state (J π i ) to final state (J π f ) for transitions placed in level scheme of 73 As are listed. 1. Relative intensity is calculated with respective to 609 kev by assuming its intensity as 100% (Continued...) (Continued...) Transition energy (E γ ), Relative Intensity (I γ ), DCO ratios (R a DCO ), Multipolarity of the transition (D/Q) and the decay from an initial state (J π i ) to the final state (J π f ) for the γ-transitions placed in the level scheme of 70 Ge are listed kev (2 + to 0 + ) which is quadrupole in nature is used as gating transition for DCO measurement and the relative intensity is calculated with respective to 1039 kev by assuming its intensity as 100%. DCO ratio for 1039 kev (gating transition) is obtained by gating on 1113 kev. Multipolarity of transitions labeled as b are assigned from the previously established work (Continued...) (Continued...)

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