As already indicated in the preceding section, the measurement of level lifetime is thus of cardinal significance in the microscopic understating of nuclear excitations and is intensely pursued through evolving and improving experimental facilities and techniques. INGA is such a facility that primarily consists of Compton-suppressed HPGe Clover detectors for practicing high-resolution gamma-ray spectroscopy in nuclear structure research. This facility was conceived, designed, and assembled within the country. It rotates between the three accelerator centers at TIFR (Mumbai), IUAC (New Delhi), and VECC (Kolkata). The setups at TIFR and IUAC can accommodate up to 24 Compton-suppressed HPGe Clover detectors that translate into a full-energy peak efficiency of ~ 5%. The setup at TIFR [1] has recently been upgraded [2] with 14 LaBr3(Ce) scintillator detectors in addition to the 24 Compton-suppressed HPGe Clover detectors, thus rendering it even more powerful for nuclear structure studies at high spins and lifetime measurements across different ranges. Similar setups of HPGe and scintillator-based detectors have also been implemented at different facilities elsewhere; the examples include that of ROSPHERE [3] at Bucharest 9 MV tandem accelerator in Romania. The FATIMA [4] setup of LaBr₃(Ce) detectors at GSI, Germany, is another facility that is directed towards direct measurement of level lifetimes using fast timing techniques.

The INGA setup at TIFR is sustained by a digitizer-based pulse processing and data acquisition system built on 12-bit, 100 MHz PIXIE-16 digitizer modules, of M/s XIA LLC, for the HPGe detectors and 12-bit, 250 MHz modules for the fast scintillators. The modules of the two sampling frequencies are housed in two different crates that are time-synchronized through a global clock module. The use of a digital data acquisition system (DDAQ), that implements pulse processing through the application of recursive algorithms on the digitized detector signals, facilitates substantially higher throughput and allows for higher event rates without pile-up. Each detection is recorded with a 48-bit time stamp and a 16-bit CFD value that are combined to calculate the total time stamp for the event. The time stamp information is conveniently used to extract the time correlation between the different detections, as is often imperative for the determination of level lifetimes. Further details on the DDAQ and its features are included in Refs. [1, 2]. The hybrid spectrometer, of HPGe and LaBr₃(Ce) detectors, at TIFR, facilitates direct measurements of level lifetimes in the range of 50 pico-sec–2 micro-sec, using the fast timing merits of the scintillators, as well as (indirect) lifetime measurements in the range of tens of femtoseconds to few pico-seconds, using the Doppler shift attenuation method (DSAM). The use of fast scintillators for lifetime measurements is now of widespread interest and is being pursued across the globe [4]. As far as the DSAM is concerned, there have been developments [5] to extend the applicability of the method beyond the cliché (thin-target-on-thick-elemental-backing, fusion-evaporation reactions) to measurements using thick targets, molecular targets, and reactions other than fusion-evaporation, to populate the nuclei of interest. Experimental campaigns using the digital INGA have been completed at the BARC-TIFR Pelletron LINAC Facility (PLF) in TIFR, Mumbai. Several experiments based on proposals from different groups within India and abroad have been carried out through the program wherein the level lifetime measurements emerged as a niche. The general aspiration of such experiments was to use the lifetime results, translated into transition probabilities, for stringently validating some excitation phenomena or unraveling different aspects of shapes and deformations in the nuclei of interest. Accordingly, the measurements have been directed at probing exotic symmetries and shapes, their evolution, and the corresponding critical points, as well as identifying angular momentum generation mechanisms that emerge from the interplay of single particles and collective degrees of freedom. Some of the physics results from this experimental campaign are highlighted in the next section.

Nuclear shapes/deformations of higher order, such as octupole, and their coupling with the single particle excitations are expected to cause complex level structures of nuclei, and investigating these is of contemporary interest in nuclear spectroscopy endeavors. The even-even Ba isotopes around A ~ 138 have substantial collective B(E3) strengths due to the octupole magic gap at Z = 56. This makes the odd-A La isotopes the ideal testing ground to study proton coupling with the octupole excitation modes in even-even Ba isotopes. Using the hybrid array of INGA coupled to LaBr3(Ce) detectors, recently, the result from a new measurement of the lifetime for 11/2⁻ state in ¹³⁷La is reported in Ref [2]. The gated γ-ray spectrum observed in the LaBr₃(Ce) scintillators was used to obtain the time differences across the 11/2⁻ state in ¹³⁷La at an excitation energy of 1004.6 keV. Three-fold coincidence data have been used to measure the lifetime of this state. The 825 keV energy gate from the HPGe clover detectors was used to select the cascade of gamma-rays across this 1004.6-keV state in LaBr₃(Ce) and generate the time-difference spectrum. Figure 2 illustrates the partial level scheme of the ¹³⁷La nucleus along with the time difference plots corresponding to the prompt-prompt (generated between the 94 keV and the 455 keV gamma-rays, not shown in the level scheme here) and the prompt-delayed coincidences. The measured [B(E3); 11/2⁻ → 5/2⁺] values in ¹³⁷La are larger than that of the lighter odd-A La isotopes. However, this is comparable with the [B(E3); 3⁻ → 0⁺] in ¹³⁶Ba, an isotone of ¹³⁷La. On the other hand, the B(E3) in ¹³³La is much smaller compared to the [B(E3); 3⁻ → 0⁺] of ¹³²Ba. The observed rise of B(E3) in ¹³⁷La was explained using results from random-phase approximation calculation. Our study has indicated a possible role of the unknown contribution of proton-neutron correlation on the evolution of [B(E3); 11/2 − → 5/2 +] strength in the odd-A La isotopes, and probing this further may be one of the pursuits in the continuing program of lifetime measurements using INGA.

The development and evolution of collectivity between the shell closures are of much interest in the context of understanding the microscopic aspects of nuclear deformation. The same has been pursued in the low excitation regime of the Sn (Z = 50) isotopes over several years and still incurs significant attention toward interpreting the associated deformation characteristics. Measurements of lifetimes of the 2⁺₁ state in ^112,120Sn [6, 7] isotopes have been undertaken using the digital INGA at TIFR following the population of the levels of interest in heavy-ion (³⁵Cl, ³²S) induced inelastic scattering. The lifetimes were extracted using the DSAM as implemented through the updated methodologies. The latter is based on using the energy-angle distribution (Fig. 3) of the recoiling nuclei along with their trajectories through the target medium to generate velocity profiles for calculating the Doppler shapes of the transitions. The systematic uncertainties on the lifetime results are restricted by the use of state-of-the-art Monte Carlo simulations for the trajectories (Fig. 3) in the framework of the TRIM (https://www.srim.org) software while using more credible and experimentally benchmarked stopping powers computed by the SRIM (https://www.srim.org) code. The calculated Doppler shapes of the transitions are least-square fitted (Fig. 3) with the experimental spectra for determining the respective level lifetimes and correspondingly the transition probabilities. The results obtained for the 2⁺₁ state of ^112,120Sn isotopes indicate enhanced collectivity that, for ¹¹²Sn, has been successfully interpreted by the Generalized Seniority Model (GSM) and the Monte Carlo Shell Model (MCSM) [7]. The latter has ascribed the enhancement to oblate deformation associated with the 2⁺₁ state, stemming from strong proton-core excitations along with enhanced proton-neutron interactions. The low-spin (quadrupole) collectivity in nuclei around and between the shell closures continues to be pursued experimentally and theoretically. There have been recent [8] calculations for the Sn isotopes and measurements, such as the aforementioned ones, are expected to help constrain the models/parametrization being developed in the exercise. Similar measurements have recently been reported for Zn [9] isotopes, around the closure at Z = 28, and ¹¹⁸Te [10] nucleus around the closure at Z = 50.

The phase transitions in nuclei correspond to those between the paradigms of shapes/deformations and the quest for the associated critical points is an intriguing one [11,12,13]. These are identified through experimental observables along with theoretical calculations using, for instance, the framework of Interacting Boson Approximation (IBA). The latter associates the shapes of the nucleus with different dynamical symmetries; the spherical vibrator with U(5), the axially symmetric rotor with SU(3), and the gamma-soft rotor with O(6). Likewise, the transition from one (shape) to another proceeds through a critical point with an associated symmetry; the critical point symmetry (CPS) associated with the transition from spherical to axially-symmetric rotor is X(5), and that with spherical to gamma-soft rotor is E(5). The experimental signatures of these symmetries include ratios of the excitation energies as well as the transition probabilities. One of the measurements using digital INGA at TIFR was directed at investigating the low-lying positive-parity structures of the ⁸²Kr [14] nucleus. Further to identifying/confirming the excitation scheme of the nucleus, level lifetimes were extracted using the updated methodologies [5] of DSAM, and transition probabilities were determined therefrom. Figure 4 illustrates the experimental and the calculated level schemes of the ⁸²Kr nucleus, following this investigation. The width of the transitions in the level scheme represents B(E2) values in the Weisskopf units (W.u.s) and normalized with the measured value of 21.3 W.u. for the B(E2) of the first 2⁺ to 0⁺ ground state. The results, particularly the ratios of the B(E2) transition probabilities between different states, are in superior overlap with those from the IBA calculations and establish E(5) symmetry in the ⁸²Kr nucleus while assertively identifying it as the critical point of phase transition between a spherical vibrator and a gamma-soft rotor. It is the maiden instance wherein the excitation energies and the transition probabilities of a nucleus have been observed to be so close to those predicted for a critical point.

The spontaneously broken symmetries determine the intrinsic shape and the associated excitation modes [15]. Magnetic rotational (MR) bands are observed in weakly deformed nuclei and signature of breaking of R_z(π) symmetry due to the tilted axis cranking. Magnetic rotation (MR) is associated with the shear structure of proton particles and neutron holes (or vice-versa). Here, the B(M1) transition strengths reduce with increasing spin in the ΔI = 1 band consisting of M1 transitions. An extension of this concept is the antimagnetic rotation (AMR) resulting from the anti-alignment of two shears, similar to the anti-ferromagnetic phenomenon in condensed matter physics, which is relatively rare compared to MR. In this case, the B(E2) transition strengths reduce with increasing spin in the ΔI = 2 band of E2 transitions. One of the experiments using the digital INGA at TIFR pertained to lifetime measurement in the sub-picosecond range for the excited states of the ¹⁰⁷Cd nucleus towards establishing the coexistence of MR and AMR modes therein [16, 17] (Fig. 5). Figure 6a, b illustrates the decreasing trends of the B(M1) and B(E2) transition probabilities with increasing spin for MR and AMR bands, respectively. The conclusive identification of the two structures followed from lifetime measurements of the levels constituting the MR and the AMR bands and the characteristic variation of the B(M1) and the B(E2) values therein. This was a unique observation where both the MR and the AMR sequences, coexisting in the same nucleus, could be interpreted to be stemming from 5-quasiparticle configurations with identical proton excitations but different neutron configurations. The study was a validation for the microscopic understanding of different mechanisms of angular momentum generation in atomic nuclei. The breaking of axial symmetry in the nuclear intrinsic state is uniquely related to two novel excitation modes, namely, chiral rotation and wobbling [18]. An experimental manifestation of chiral symmetry breaking is the observation of near-degenerate dipole bands with similar electromagnetic properties and moments of inertia (MOI). Spectroscopic studies of degenerate dipole bands in ^106,108Ag isotopes have been carried out, using the digital INGA at TIFR, to understand the role of triaxiality in the excitation schemes of these isotopes [19, 20]. The lifetime measurements of the two nearly-degenerate bands of ¹⁰⁶Ag led to the conclusion that these are characterized by similar transition probabilities, B(M1) and B(E2), while differing in their MOIs [18]. This has been a unique observation and is expected to facilitate new insights for such doublet sequences that often characterize the level structures of transitional nuclei.

Another highlight of the present experimental campaign, using the digital INGA setup at TIFR, has been the spectroscopic study of nuclei in the vicinity of ¹³²Sn (Z = 50, N = 82) following their population in fusion/transfer-induced fission processes. In one such endeavor, the prompt-delayed coincident data from the experiment at INGA complements the fragment-gated gamma spectroscopy data from EXOGAM-VAMOS + + and facilitated firm assignments of the transitions in the level scheme of ¹³²Te beyond the isomers therein [21]. These measurements have been carried out to investigate the competition of neutron and proton pairs for generating the high spin states in ¹³²Te. The experimental study helps in understanding the impact of the nn, pp, and pn interactions as used in the shell model calculations towards interpreting the level scheme of ¹³²Te. The exercise aids in understanding the deficiencies in the theoretical framework while noting the increased discrepancies between the calculated and the experimental level energies of lighter Te isotopes. A similar study, that addresses the shell model interpretation of nuclei in the vicinity of the shell closures, has also been carried out for nuclei near ⁶⁸Ni using a multi-nucleon transfer reaction [22].

Further to those described in the preceding text, there have been other level lifetime measurements, such as for sdpf nuclei in A ~ 30 region [23,24,25], using the digital INGA setup at TIFR along with the aforementioned updated methodologies of DSAM. These have been in the context of investigating the single-particle excitations for the nuclei of interest while probing the relevant interactions in the shell model framework. Some of these studies have also unraveled [23, 25] the development of collectivity and deformation characteristics in these light mass nuclei thus adding to a detailed perspective on their structure across different regimes of excitations. These results have established important benchmarks for the corresponding residual interactions that are used in the shell model calculations of the level energies and the transition probabilities.

The preceding discussions intend to assert that the lifetime measurements are and will be of sustained significance in nuclear structure research while facilitating stringent conclusions on the many phenomena manifested by the excited nuclei. In the same context, facilities such as INGA are of superlative importance in the progress of the subject and empower the national fraternity with state-of-the-art equipment and the infrastructure to realize its research aspirations. The ecosystem immensely benefits the young researchers who can access advanced radiation detectors, digital signal processing hardware, and computational resources that engineer their growth towards assuming scientific leadership in the national as well as the international academia. The experimental programs being undertaken at INGA are aligned with global interests in the area of nuclear spectroscopy. The accomplishments therefrom notwithstanding, it is of paramount importance to keep developing the facility and evolve its merits for addressing measurements that necessitate improved sensitivity and/or better efficiency. These could pertain to, for instance, exotic phenomena exhibited by nuclei at extreme excitations, nuclear structure inputs to understand the evolution of the universe, or constraining nuclear matrix elements for neutrinoless double beta decay. The pathways envisaged include augmenting the setup with more ancillary detectors, preferably a modular structure that renders them portable for transportation between the three accelerator centers housing INGA. The facilities for nuclear-level lifetime measurements could be expanded with the implementation of a setup for the Recoil Distance Method (RDM) as well as with the use of gas-backed targets for DSAM. The setup for pursuing RDM has already been implemented at IUAC, New Delhi, and integrated with the INGA therein [26]. The use of gas as the stopping medium would incur larger stopping times and thus extend the range of DSAM to tens of pico-seconds. The use of segmented scintillator detectors may help improve the timing resolution for direct fast timing measurements. One of the important and recent developments has been a hybrid array consisting of an Annular Double Sided Si Detector (ADSSD) integrated with the digital INGA setup at TIFR [27]. Such a setup allows for particle-gamma coincidence measurements that facilitate the choice of excited states, for analysis, and help constrain their feeding; this is one of the significant inputs for lifetime measurements using DSAM with direct reactions. Somepossible physics that could be pursued under the lifetime measurement program are investigating (i) the structure of light to medium nuclei to test the predictions of new ab initio theories and alpha-cluster states, (ii) nuclear shape-coexistence and shape transition phenomena across the nuclear landscape, (iii) low-lying vibrational modes and their coupling with the odd particle, and (iv) the wobbling and chiral modes in triaxial nuclei. Measurements of level lifetimes in the heavier (trans-lead) nuclei could be another prospective agenda; these would be directed at observing phenomena such as magnetic rotation and chiral rotation that have been conspicuously sparse in these heavy nuclei [28]. Lifetime measurements for structures associated with higher order symmetries, such as octupole, could be illustrative in deciphering their stability and are listed as prospective pursuits at INGA. The associated developments are also expected to help diversify the physics program pursued at INGA with Indian accelerator facilities and expand it to other domains of nuclear physics and its applications, such as in medical physics and material studies. In addition, these developments will also encourage new collaborations from India with research facilities in Asia [29,30,31,32] and other international facilities that are related to nuclear structure studies.

The data and figures from published materials belong to the authors of each publication. The other data and figures are available from the authors upon reasonable request.

The authors would like to acknowledge the support of INGA PICC and the contribution of the INGA collaborators from TIFR, IUAC, BARC, SINP, UGC-DAE CSR (Kolkata Centre), VECC, IITs and Universities for the success of INGA campaign at TIFR. About 65 scientists, including 30 Ph.D. students from different universities as well as research institutes within India and abroad, are involved in the experimental campaigns. We are thankful to the Pelletron LINAC Facility staff for providing excellent beams during all experiments of the campaigns.

This work was partially funded by the Department of Atomic Energy, Government of India (Project Identification No. RTI 4002) and the Department of Science and Technology, Government of India (No. IR/S2/PF-03/2003-II) and (No. IR/S2/PF-03/2003-III).

Authors and Affiliations

Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai, 400005, India
Rudrajyoti Palit
UGC-DAE Consortium for Scientific Research, Kolkata Centre, Kolkata, 700098, India
Rajarshi Raut

Contributions

RP and RR wrote the manuscript. All authors proofread and approved the final version of the manuscript.

Corresponding author

Correspondence to Rudrajyoti Palit.

Competing interests

The authors declare that they have no competing interests.

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