Search for Jacobi shape transition in A \sim30 nuclei
Balaram Dey, C. Ghosh, Deepak Pandit, A.K. Rhine Kumar, S. Pal, V. Nanal, R.G. Pillay, P. Arumugam, S. De, G. Gupta, H. Krishnamoorthy, E.T. Mirgule, Surajit Pal, P.C. Rout
aa r X i v : . [ nu c l - e x ] A ug Search for Jacobi shape transition in A ∼ nuclei Balaram Dey, C. Ghosh, Deepak Pandit, A.K. Rhine Kumar, S. Pal, V. Nanal, ∗ R.G. Pillay, P.Arumugam, S. De, G. Gupta, H. Krishnamoorthy, E.T. Mirgule, Surajit Pal, and P.C. Rout Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai-400005, India Variable Energy Cyclotron Centre, 1/AF-Bidhannagar, Kolkata-700064, India Department of Physics, Cochin University of Science and Technology, Cochin-682022, Kerala, India. Pelletron Linac Facility, Tata Institute of Fundamental Research, Mumbai-400005, India Department of Physics, Indian Institute of Technology, Roorkee-247667, India Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai-400085, India Indian Neutrino Observatory, Tata Institute of FundamentalResearch and Homi Bhabha National Institute, Mumbai-400085, India (Dated: October 8, 2018)This paper reports the first observation of the Jacobi shape transition in P using high energy γ -rays from the decay of giant dipole resonance (GDR) as a probe. The measured GDR spectrum inthe decay of P shows a distinct low energy component around 10 MeV, which is a clear signatureof Corioli’s splitting in a highly deformed rotating nucleus. Interestingly, a self-conjugate α -clusternucleus Si, populated at similar initial excitation energy and angular momentum, exhibits a vastlydifferent GDR line shape. Even though the angular momentum of the compound nucleus Si ishigher than the critical angular momentum required for the Jacobi shape transition, the GDRlineshape is akin to a prolate deformed nucleus. Considering the present results for Si and similarobservation recently reported in S, it is proposed that the nuclear orbiting phenomenon exhibitedby α -cluster nuclei hinders the Jacobi shape transition. The present experimental results suggest apossibility to investigate the nuclear orbiting phenomenon using high energy γ -rays as a probe. Many body quantum systems like atomic nuclei provide a unique opportunity to explore a variety of phenom-ena arising due to interplay of different physical processes, particularly at high excitation energy ( E ∗ ) and angularmomentum ( J ). One such interesting phenomenon is the Jacobi shape transition, where beyond a critical angularmomentum ( J C ), an abrupt shape change from non-collective oblate shape to collective triaxial or prolate shape takesplace [1]. The study of exotic Jacobi shapes in nuclei has been a topic of considerable interest [2, 3]. The Jacobishape transition is expected to occur in light and medium mass nuclei, where high rotational frequencies are achievedbefore the excited nucleus can undergo fission. Further, it is expected that the Jacobi shape transition should bea common feature over a wide range of nuclei. Experimentally, the Jacobi shape transition has been observed in afew light mass nuclei A ∼
45 [4–7] via the γ -decay of giant dipole resonance (GDR). It is known that the GDR isthe cleanest, and hence most extensively used, probe to study the properties of nuclei at high temperature ( T ) and J [8]. The GDR can be understood macroscopically as an out-of-phase oscillation between protons and neutrons,and microscopically in terms of coherent particle-hole excitations. The GDR γ -emission occurs at the early stage ofcompound nucleus (CN) decay and can probe the nuclear shape. The GDR components corresponding to vibrationalong and perpendicular to the axis of rotation are differently affected by the Corioli’s force. As a result the GDRstrength function splits into multiple components with a narrow well separated peak around 8-10 MeV [4], which is anunambiguous signature of the Jacobi shape transition. It should be mentioned that the search for Jacobi shapes hasalso been made through studies of quasi-continuum gamma radiation [9]. However, indications of highly deformedshapes could not be uniquely ascribed to the Jacobi shape.While many of the observed features of nuclei at high E ∗ , J can be understood in terms of rotating liquid dropmodel (RLDM) and mean field approach, it is well known that nuclei also exhibit cluster structure [10–13]. Theinfluence of clustering in the stellar nucleosynthesis has been a long-standing question in nuclear astrophysics [14–16].Nuclear orbiting phenomena involving formation of a long-lived dinuclear molecular complex, with a strong memoryof the entrance channel, has been observed in reactions involving self conjugate α -cluster nuclei [17, 18]. Such anorbiting dinuclear system can attain complicated exotic shapes as compared to a shape equilibrated compound nucleus[10, 17, 19–21]. Interestingly, recent studies of GDR spectrum from the S nucleus populated with
J > J C in thereaction Ne+ C, did not show evidence of the Jacobi shape transition [7, 23] and the result was interpreted interms of the formation of O + O molecular structure in a superdeformed state of S. The observation of a narrowresonance in Mg+ Mg at J = 36 ¯ h [22] was interpreted in terms of the highly deformed shape corresponding toa molecular state, but no clear signature of the Jacobi shape transition was observed. ∗ e-mail:[email protected] FIG. 1: (Color online) Experimental fold distribution (symbol) together with that from the SMCC calculations (line) for F+ C and O+ C reactions.
Therefore, experimental studies of the exotic shapes of different nuclei with
J > J C are crucial to understand thedifferent mechanisms like the nuclear orbiting, cluster formation and Jacobi shape transition. The aim of the presentstudy is to investigate the deformed shapes of a α -cluster ( Si) and a non- α -cluster ( P) nuclei at high J usingthe GDR as a probe. This work also addresses the open question whether the Jacobi shape transition is a generalphenomenon in light mass nuclei.The experiments were performed using pulsed beams of F (at E lab =127 MeV) and O (at E lab =125 MeV) fromthe Pelletron Linac Facility (PLF), Mumbai bombarding a self-supporting C target (400 µ g/cm ). The high energy γ -rays in the region of 5-30 MeV were measured using an array of seven close packed hexagonal BaF detectors (each20 cm long with face-to-face distance of 9 cm) mounted at 125 with respect to the beam direction and at a distance of57 cm from the target position. A 14-element BGO multiplicity filter (hexagonal, 6.3 cm long and 5.6 cm face-to-face)was mounted in a castle geometry surrounding the target ( ∼
60% efficiency at 662 keV), for measuring the multiplicity( M ) of low energy discrete γ -rays to extract the angular momentum information. The BaF array was surroundedby an annular plastic detector which was used as a cosmic ray veto. Detector arrays, upstream collimators and thebeam dump (kept at ∼ detector was integrated in two different gates of width 200 ns ( E short ) and 2 µ s ( E long ) for pileuprejection using pulse shape discrimination (PSD) and energy measurement, respectively. The time-of-flight (TOF)of each BaF detector with respect to the RF pulse was used to reject neutron events. For each event E short , E long ,BaF -TOF of each BaF detector were recorded together with the fold F (number of BGO detectors fired for E th >
120 keV within a 50 ns coincidence window) and BGO-TOF with respect to the RF pulse [24]. The energy calibrationof the BaF detector array was obtained using low energy radioactive sources and was linearly extrapolated to highenergies. The gain stability of the BaF detectors was found to be within ± γ -ray spectra for different folds are generated in offline analysis after incorporating correctionsdue to chance coincidence and Doppler effect arising from the finite recoil velocity of the residues. The γ -ray spectrafor F ≥ h T i and h J i following the procedure in Ref. [25]. In both systems, the data corresponding to lower folds( F ≤
3) were not considered as it can have contributions from radioactivity and extraneous background. The opticalmodel parameters are taken from Ref. [27–29] and Ignatyuk level density prescription [30] is used with ˜a = A /7MeV − [31]. The effective moment of inertia is assumed to be I eff = I (1 + δ J + δ J ), where I (= A / r ) isthe rigid-body moment of inertia, r is radius parameter, δ and δ are deformation parameters. The residue spindistribution ( J res ) is calculated starting from the standard J CN distribution and is converted to the multiplicity M using the relative decay probability ( P r ) of dipole and quadrupole transitions as a parameter. The M distributionis then converted to the fold ( F ) distribution incorporating the BGO array efficiency and crosstalk probability asdescribed in Ref. [32]. All three parameters, namely, P r , δ and δ are varied to fit the experimentally observed folddistribution. The fold distributions thus calculated with the SMCC for both systems are shown in Fig. 1 togetherwith the data. It is important to note that both reactions are studied in the same setup and with a similar analysis,to rule out any systematic factors that could affect the data.The γ -ray spectrum in the SMCC is calculated assuming ∼ FIG. 2: (Color online) Fold gated high energy γ -ray spectra (symbols) with the best fit SMCC calculation (line) for (a) Pand (b) Si; corresponding divided plots are shown in panel (c) and (d). Divided plot for Si with F ≥ as (e − E γ /E ) with E = 1.1[( E lab - V c )/ A p ] . , where E lab , V c and A p are the beam energy, Coulomb barrier and theprojectile mass, respectively. The bremsstrahlung spectrum folded with the detector response function was added tothe calculated GDR spectrum for comparison with data. The goodness of the fit is achieved by χ minimization andvisual inspection in the energy range of E γ = 7 - 25 MeV. Fold gated high energy γ -ray spectra and the divided plots(generated using a γ -ray spectrum calculated with an arbitrary constant dipole strength of 0.2 W.u. folded with theBaF array response) together with the best fit statistical model calculations for both P and Si are shown in Fig. 2.The GDR spectrum of P could be not be fitted with prolate/oblate shape (2-component Lorentzian function) or atriaxial shape (3-component Lorentzian function). The observed spectrum has five Lorentzian components, resultingfrom the Jacobi shape transition. To restrict the fitting window (for large no. of parameters), initial values forcentroid energy ( E i ), width (Γ i ) and strength ( S i ) were taken from Ref. [34] and then varied individually within alimited range to achieve the best fit. In case of Si, a two component strength function corresponding to a prolateshape describes the data well. The best fit GDR parameters for both the nuclei are given in Table I. It should be
TABLE I: Best fit GDR parameters from the SMCC analysis.System h J i (¯ h ) h T i (MeV) E GDR (MeV) Γ GDR (MeV) S GDR P 22(6) 2.2(3) 9.1(1) 2.2(1) 0.18(2)14.2(3) 4.4(2) 0.30(1)18.2(4) 7.3(4) 0.18(2)20.0(6) 8.8(5) 0.14(3)23.0(8) 9.6(8) 0.16(3) Si 21(6) 2.1(3) 14.6(3) 6.0(3) 0.44(4)24.6(8) 10.0(7) 0.62(3) mentioned that the GDR lineshape is not expected to be very sensitive to the level density parameter [35]. In thepresent case, the extracted GDR parameters corresponding to ˜a = A / A /
8, are same within fitting errors. Theeffect of direct reactions like pre-equilibrium emission, incomplete fusion etc. is not considered, since it has beenshown to be negligible for O+ C at the present beam energy [36]. ← β → γ = −180 ° −160 ° −140 ° γ = −120 ° −100 ° −80 ° γ = −60 ° −40 ° −20 ° γ = 0 ° T = 2 . J = 22 ¯ h ← β → γ = −180 ° −160 ° −140 ° γ = −120 ° −100 ° −80 ° γ = −60 ° −40 ° −20 ° γ = 0 ° T = 2 . J = 21 ¯ h (a) (b)FIG. 3: (Color online) The free energy surfaces of (a) P and (b) Si for the measured T and J (contour line spacing is0.2 MeV). Here, γ = 0 ◦ ( − ◦ ) represent the non-collective (collective) prolate shape and γ = − ◦ ( − ◦ ) represent thenon-collective (collective) oblate shape. The most probable shape is represented by a filled circle. Most noteworthy is the striking difference between the GDR spectra in two reactions leading to P and Si nuclei.Both P and Si, populated at the same initial excitation energy ( E ∗ ∼
70 MeV) and with angular momentum
21 ¯ h ( ± h ). The J C from systematics in Ref. [2] are 19 ¯ h and 17 ¯ h for P and Si, respectively. While P spectrum shows the expected multicomponent character arising due to the Corioli’s splitting with a distinct lowenergy peak at ∼ γ -ray spectrum of Si does not show evidence of the Jacobi shape transition. It can beseen from the Fig. 1 that Si yield shows significant enhancement at higher folds as compared to P. Therefore, themeasured fold distribution together with the fact that J C is lower for Si than that for P, makes the non-occurrenceof Jacobi shape transition in Si very fascinating. Further, the γ -ray spectrum of Si for F ≥ h J i = 24 ¯ h ( ± h ) was also found to have same shape and no peak was visible around 10 MeV [see inset of Fig. 2(d)].The measured GDR strength functions are compared with thermal shape fluctuation model (TSFM) calculationscorresponding to the measured h T i and h J i values given in Table I. The details of the TSFM calculation are discussedin the Refs. [37–40], where shape fluctuations are treated by evaluating the expectation values of the observables(over the deformation degrees of freedom) with their probability given by the Boltzmann factor [exp( − F/T )]. Thefree energy ( F ) is calculated within a microscopic-macroscopic approach by tuning the angular frequency to get thedesired J . The calculated free energy surfaces (FES) are shown in Fig. 3, where it can be seen that the predictedequilibrium shapes for both P and Si are similar and both the nuclei are therefore expected to show similarbehaviour -namely, the Jacobi shape transition. The calculated GDR cross-sections ( σ T SF M ) are compared with thecorresponding best fit statistical model calculation ( σ stat ) in Fig. 4. Since the absolute cross-section is not measuredin the present experiment, σ T SF M was normalized to the total σ stat in the energy region of E γ = 7 - 25 MeV [41].The variance in σ stat is calculated from the errors of the best fit parameters. The P data is in qualitative agreementwith the TSFM predictions, but this is not the case for Si. The TSFM predicts a low energy component ( ∼ Si, which is not corroborated by the data. Further, the TSFM calculations carried out without the shelleffects are also shown in the same figure. It is seen that shell effects do not significantly affect the GDR cross-sectionat the measured T , J . The TSFM calculation does not include the pairing effect, which is expected to be negligibleat T ∼ Si at high J is anamolous as compared to Pand this discrepancy can not be understood in terms of TSFM or microscopic factors like shell or pairing effects. Itshould be noted that O+ C reaction has entrance channel isopsin T = 0, which is expected to suppress the GDRyield [42] but is not expected to affect the shape of the GDR strength function.Recently, similar observation- namely, the absence of Jacobi shape transition, was reported in S populated via Ne+ C reaction [23]. In both these cases ( S and Si), projectile-target involve self-conjugate α -cluster nuclei. Asmentioned earlier, the reactions involving these nuclei are shown to exhibit orbiting phenomenon leading to formationof quasi-molecular states [19, 20]. The orbiting behaviour in O + C at E lab = 125 MeV was reported earlierin charged particle studies [18]. In such molecular states, the configuration will have a two body rotor with massconcentrated on the periphery as opposed to a deformed nucleus with most of the mass at the center. Hence, themoment of inertia corresponding to a molecular resonance state is expected to be larger and consequently the angularfrequency would be smaller. Thus, the formation of the dinuclear complex due to orbiting may suppress the Jacobishape transition. Further, in case of quasi-molecular resonances there would be an interplay of rotational motion ofthe dinuclear complex and vibrational motion of constituent nuclei, which would result in the fragmented strength[43]. It should be pointed out that the net excitation energy as well as effective T and J for such a state can not FIG. 4: (Color online) The best fit statistical model input cross-section (filled symbols) compared to TSFM calculations with(continuous line) and without (dashed line) Shell effect. be estimated in a simple manner. Moreover, the statistical model analysis or TSFM, which assumes a formation ofequilibrated CN, is not suitable to describe the data. Detailed theoretical calculations are required to understandwhether the fragile correlations leading to molecular configurations survive thermal fluctuations. In addition, therole of possible binary shapes on GDR, at large excitations needs to be investigated. It is important to note thatthe S GDR data [7, 23] has been analyzed only within the statistical model framework. However, deformationsdeduced for both S, Si from the conventional statistical model analysis are large ( β > .
6) and point towards theelongated structure. It should be mentioned that the earlier data reporting the signature of orbiting in Ref. [36] fromthe charged particle spectra, have shown the co-existence of molecular resonance states with equilibrated compoundnucleus formation. In such a scenario, it is possible that high J components of the entrance channel are predominantlycontributing to the orbiting state and consequently the CN is formed with J < J C . In the present experiment, γ -raysfrom CN with h J i ≤
15 ¯ h (corresponding to F <
3) could not be unambiguously extracted.In summary, the measurement of high energy γ -rays from the decay of giant dipole resonance in P nucleus anda self-conjugate α -cluster nucleus Si, populated at same initial excitation energy and h J i > J C was carried out tostudy the Jacobi shape transition. The measured GDR spectrum in the decay of P shows a distinct low energycomponent around 10 MeV, which is a clear signature of the Corioli’s splitting in a highly deformed rotating nucleus.This first observation of the Jacobi shape transition in P, together with earlier results in A ∼ −
50 nulclei, showthat Jacobi shape transition is a general feature of nuclei in light mass region. The observed GDR strength functionin P can be qualitatively explained by the TSFM. An anomalous behaviour is observed in the case of Si, wherethe GDR lineshape can be explained as 2-components to a prolate deformed nucleus, and does not exhibit signatureof Jacobi shape transition. Based on this data and similar recent results in S, it is proposed that the nuclearorbiting phenomenon exhibited by α -cluster nuclei, hinders the Jacobi shape transition. The study of the GDR inself-conjugate α -cluster CN populated through different entrance channels comprising α -cluster and non- α cluster,would be important to understand the role of orbiting in nuclear structure. The present experimental results suggesta possibility to investigate the nuclear orbiting phenomenon using high energy γ -rays as a probe. Acknowledgement
We would like to thank Mr. M.S. Pose, Mr. K.S. Divekar, Mr. M.E. Sawant, Mr. Abdul Quadir, Mr. R. Kujur forhelp with experimental setup, Mr. R.D. Turbhekar for target preparation and the PLF staff for the smooth operationof the accelerator. AKRK acknowledges the financial support from the DST-INSPIRE Faculty program (India) andRIKEN Supercomputer HOKUSAI GreatWave System for the numerical calculations. PA acknowledges financialsupport from the SERB (India), DST/INT/POL/P-09/2014. [1] R Beringer and W J Knox, Phys. Rev. 121 (1961) 1195.[2] W. D. Meyers and W. J. Swiatecki, Acta. Phys. Pol. B 32 (2001) 1033.[3] Mazurek et al., Phys. Rev. C 91 (2015) 034301.[4] M. Kicihska-Habior et al., Phys. Lett. B. 308 (1993) 225. ∼∼