Over the last four decades, the isoscalar giant monopole resonance (ISGMR) was extensively studied worldwide, especially at the Texas A&M University (TAMU) Cyclotron Institute, the Research Center for Nuclear Physics (RCNP) and recently at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), South Africa, through small angle (including 0 degrees) inelastic alpha-scattering measurements at 240, 386, and 196 MeV, respectively. In all the available datasets published by the different facilies, noticeable differences in the isoscalar giant monopole (IS0) strength distributions were observed. This paper focuses only on the two extreme cases: the light deformed 24Mg and the heavy spherical 208Pb to summarize discrepancies between the different results.

Background: Over the past two decades high energy -resolution inelastic proton scattering studies were used to gain an understanding of the origin of fine structure observed in the isoscalar giant quadrupole resonance (ISGQR) and the isovector giant dipole resonance (IVGDR). Recently, the isoscalar giant monopole resonance (ISGMR) in Ni-58, Zr-90,Sn-120, and Pb-208 was studied at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) by means of inelastic alpha-particle scattering at very forward scattering angles (including 0). The good energy resolution of the measurement revealed significant fine structure of the ISGMR. Objective: To extract scales by means of wavelet analysis characterizing the observed fine structure of the ISGMR in order to investigate the role of different mechanisms contributing to its decay width. Methods: Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental energy scales are compared to different theoretical approaches performed in the framework of quasiparticle random phase approximation (QRPA) and beyond-QRPA including complex configurations using both non -relativistic and relativistic density functional theory. Results: All models highlight the role of Landau fragmentation for the damping of the ISGMR especially in the medium -mass region. Models which include the coupling between one-particle-one-hole (1p -1h) and two-particle-two-hole (2p -2h) configurations modify the strength distributions and wavelet scales indicating the importance of the spreading width. The effect becomes more pronounced with increasing mass number. Conclusions: Wavelet scales remain a sensitive measure of the interplay between Landau fragmentation and the spreading width in the description of the fine structure of giant resonances. The case of the ISGMR is intermediate between the IVGDR, where Landau damping dominates, and the ISGQR, where fine structure originates from coupling to low-lying surface vibrations.

Background: Over the past two decades high energy-resolution inelastic proton scattering studies were used to gain an understanding of the origin of fine structure observed in the isoscalar giant quadrupole resonance (ISGQR) and the isovector giant dipole resonance (IVGDR). Recently, the isoscalar giant monopole resonance (ISGMR) in 58Ni, 90Zr, 120Sn, and 208Pb was studied at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) by means of inelastic α-particle scattering at very forward scattering angles (including 0∘). The good energy resolution of the measurement revealed significant fine structure of the ISGMR. Objective: To extract scales by means of wavelet analysis characterizing the observed fine structure of the ISGMR in order to investigate the role of different mechanisms contributing to its decay width. Methods: Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental energy scales are compared to different theoretical approaches performed in the framework of quasiparticle random phase approximation (QRPA) and beyond-QRPA including complex configurations using both non-relativistic and relativistic density functional theory. Results: All models highlight the role of Landau fragmentation for the damping of the ISGMR especially in the medium-mass region. Models which include the coupling between one-particle–one-hole (1p-1h) and two-particle–two-hole (2p-2h) configurations modify the strength distributions and wavelet scales indicating the importance of the spreading width. The effect becomes more pronounced with increasing mass number. Conclusions: Wavelet scales remain a sensitive measure of the interplay between Landau fragmentation and the spreading width in the description of the fine structure of giant resonances. The case of the ISGMR is intermediate between the IVGDR, where Landau damping dominates, and the ISGQR, where fine structure originates from coupling to low-lying surface vibrations.1 MoreReceived 8 September 2023Accepted 22 December 2023DOI:https://doi.org/10.1103/PhysRevC.109.014325©2024 American Physical SocietyPhysics Subject Headings (PhySH)Nuclear structure & decaysResearch AreasNuclear structure & decaysResearch AreasDirect reactionsInelastic scattering reactionsLow & intermediate energy heavy-ion reactionsModels & methods for nuclear reactionsNuclear density functional theoryNuclear structure & decaysNuclear Physics

Extensive experimental investigations into understanding the fine structure of giant resonances in nuclei across the periodic table have been carried out in recent years using the state-of-the-art K600 magnetic spectrometer of iThemba LABS, Cape Town, South Africa. Based on the established results in comparison to various theoretical calculations, it has been found that the fine structure observed in different giant resonances, namely Isoscalar Giant Quadrupole Resonance (ISGQR), Isovector Giant Dipole Resonance (IVGDR) and Isoscalar Giant Monopole Resonance (ISGMR), in light nuclei such as 40 Ca, 28 Si and 27 Al is dominated by Landau damping although signatures for the role of the spreading width are also found. In this report, characteristic energy scales extracted in light nuclei are compared with the state-of-the-art theoretical calculations, while the fine structures results obtained are compared using semblance analysis to search for possible signatures of common fragmentation patterns induced by Landau damping and coupling to 2p-2h states obtained from different giant resonances.

Background: Inelastic alpha-particle scattering at energies of a few hundred MeV and very-forward scattering angles including 0 degrees has been established as a tool for the study of the isoscalar giant monopole (IS0) strength distributions in nuclei. This compressional mode of nuclear excitation can be used to derive the incompressibility of nuclear matter.Purpose: An independent investigation of the IS0 strength in nuclei across a wide mass range was performed using the 0 degrees facility at iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), South Africa, to understand differences observed between IS0 strength distributions in previous experiments performed at the Texas A&M University (TAMU) Cyclotron Institute, USA and the Research Center for Nuclear Physics (RCNP), Japan.Methods: The isoscalar giant monopole resonance (ISGMR) was excited in 58Ni, 90Zr, 120Sn, and 208Pb using alpha-particle inelastic scattering with a 196 MeV alpha beam and scattering angles theta Lab = 0 degrees and 4 degrees. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered alpha particles. The IS0 strength distributions in the nuclei studied were deduced with the difference-of-spectra (DoS) technique including a correction factor for the 4 degrees data based on the decomposition of L > 0 cross sections in previous experiments.Results: IS0 strength distributions for 58Ni, 90Zr, 120Sn, and 208Pb are extracted in the excitation-energy region Ex = 9-25 MeV. Using correction factors extracted from the RCNP experiments, there is a fair agreement with their published IS0 results. Good agreement for IS0 strength in 58Ni is also obtained with correction factors deduced from the TAMU results, while marked differences are found for 90Zr and 208Pb.Conclusions: Previous measurements show significant differences in the IS0 strength distributions of 90Zr and 208Pb. This work demonstrates clear structural differences in the energy region of the main resonance peaks with possible impact on the determination of the nuclear matter incompressibility presently based on the IS0 centroid energies of these two nuclei. The results also suggest that, for an improved determination of the incompressibility, theoretical approaches should aim at a description of the full strength distributions rather than the centroid energy only.

The iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) is a centre of expertise and innovation in the field of nuclear-structure physics and is a leader in several high-impact studies. One of the highlights of these nuclear-structure experiments is the study of the broad structure of the IsoVector Giant Dipole Resonance (IVGDR) in the rare-earth region. Proton inelastic scattering experiments with E p = 200 MeV were performed on the even-even Nd isotope chain and 152 Sm at very forward scattering angles including zero degrees with the K600 magnetic spectrometer. The evolution of the shape of the IVGDR in the transition from spherical to deformed nuclei was investigated. One of the goals of this highlighted study was to confirm the K -splitting observed in previous photo-absorption measurements from Saclay. Significant discrepancies were found between the direct (γ, xn) data obtained at Saclay and the equivalent photo-absorption cross sections obtained using (p, p′) data from the K600. Furthermore, discrepancies exist for several nuclei between photo-absorption data taken at the Saclay and Livermore laboratories. These discrepancies, possible reasons for them and future investigations will be presented and discussed.

Background: Inelastic $\ensuremath{\alpha}$-particle scattering at energies of a few hundred MeV and very-forward scattering angles including 0\ifmmode^\circ\else\textdegree\fi{} has been established as a tool for the study of the isoscalar giant monopole (IS0) strength distributions in nuclei. This compressional mode of nuclear excitation can be used to derive the incompressibility of nuclear matter.Purpose: An independent investigation of the IS0 strength in nuclei across a wide mass range was performed using the ${0}^{\ensuremath{\circ}}$ facility at iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), South Africa, to understand differences observed between IS0 strength distributions in previous experiments performed at the Texas A University (TAMU) Cyclotron Institute, USA and the Research Center for Nuclear Physics (RCNP), Japan.Methods: The isoscalar giant monopole resonance (ISGMR) was excited in $^{58}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ using $\ensuremath{\alpha}$-particle inelastic scattering with a 196 MeV $\ensuremath{\alpha}$ beam and scattering angles ${\ensuremath{\theta}}_{\text{Lab}}={0}^{\ensuremath{\circ}}$ and ${4}^{\ensuremath{\circ}}$. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered $\ensuremath{\alpha}$ particles. The IS0 strength distributions in the nuclei studied were deduced with the difference-of-spectra (DoS) technique including a correction factor for the ${4}^{\ensuremath{\circ}}$ data based on the decomposition of $L0$ cross sections in previous experiments.Results: IS0 strength distributions for $^{58}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are extracted in the excitation-energy region ${E}_{\mathrm{x}}=9--25$ MeV. Using correction factors extracted from the RCNP experiments, there is a fair agreement with their published IS0 results. Good agreement for IS0 strength in $^{58}\mathrm{Ni}$ is also obtained with correction factors deduced from the TAMU results, while marked differences are found for $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$.Conclusions: Previous measurements show significant differences in the IS0 strength distributions of $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$. This work demonstrates clear structural differences in the energy region of the main resonance peaks with possible impact on the determination of the nuclear matter incompressibility presently based on the IS0 centroid energies of these two nuclei. The results also suggest that, for an improved determination of the incompressibility, theoretical approaches should aim at a description of the full strength distributions rather than the centroid energy only.

The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under 0∘ is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.

Background: In highly deformed nuclei, there is a noticeable coupling of the isoscalar giant monopole resonance (ISGMR) and the K = 0 component of the isoscalar giant quadrupole resonance (ISGQR), which results in a double peak structure of the isoscalar monopole (IS0) strength (a narrow low-energy deformation-induced peak and a main broad ISGMR part). The energy of the narrow low-lying IS0 peak is sensitive to both the incompressibility modulus K(infinity )and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Purpose: This study aims to investigate the two-peaked structure of the ISGMR in the prolate Mg-24 and oblate Si-28 nuclei and identify among a variety of energy density functionals based on Skyrme parametrizations the one which best describes the experimental data. This will allow for conclusions regarding the nuclear incompressibility. Because of the strong IS0/IS2 coupling, the deformation splitting of the ISGQR will also be analyzed. Methods: The ISGMR was excited in Mg-24 and Si-28 using alpha-particle inelastic scattering measurements acquired with an E-alpha = 196 MeV beam at scattering angles theta(Lab) = 0 degrees and 4 degrees. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered alpha particles. An experimental energy resolution of approximate to 70 keV (FWHM) was attained, revealing fine structure in the excitation-energy region of the ISGMR. The IS0 strength distributions in the nuclei studied were obtained with the difference-of-spectra (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces. Results: IS0 strength distributions for Mg-24 and Si-28 are extracted and compared to previously published results from experiments with a lower energy resolution. With some exceptions, a reasonable agreement is obtained. The IS0 strength is found to be separated into a narrow structure at about 13-14 MeV in Mg-24, 17-19 MeV in Si-28, and a broad structure at 19-26 MeV in both nuclei. The data are compared with QRPA results. The results of the calculated characteristics of IS0 states demonstrate the strong IS0/IS2 coupling in strongly prolate Mg-24 and oblate Si-28. The narrow IS0 peaks are shown to arise due to the deformation-induced IS0/IS2 coupling and strong collective effects. The cluster features of the narrow IS0 peak at 13.87 MeV in Mg-24 are also discussed. The best description of the IS0 data is obtained using the Skyrme force SkP(delta) with an associated low nuclear incompressibility K-infinity = 202 MeV allowing for both the energy of the peak and integral IS0 strength in Mg-24 and Si-28 to be reproduced. The features of the ISGQR in these nuclei are also investigated. An anomalous deformation splitting of the ISGQR in oblate Si-28 is found. The observed structure of ISGQR in Mg-24 is described. Conclusions: The ISGMR and ISGQR in light deformed nuclei are coupled and thus need to be described simultaneously. Only such a description is relevant and consistent. The deformation-induced narrow IS0 peaks can serve as an additional sensitive measure of the nuclear incompressibility.

S. D. Olorunfunmi, R. Neveling, J. Carter, P. von Neumann-Cosel, I. T. Usman, P. Adsley, A. Bahini, L. P. L. Baloyi, J. W. Brümmer, L. M. Donaldson, H. Jivan, N. Y. Kheswa, K. C. W. Li, D. J. Maŕin-Lámbarri, P. T. Molema, C. S. Moodley, G. G. O’Neill, P. Papka, L. Pellegri, V. Pesudo, E. Sideras-Haddad, F. D. Smit, G. F. Steyn, A. A. Aava, F. Diel, F. Dunkel, P. Jones, and V. Karayonchev School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa iThemba Laboratory for Accelerator Based Sciences, Somerset West 7129, South Africa Institute für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany Department of Physics, University of Stellenbosch, Matieland 7602, South Africa Institut de Physique Nucléaire d’Orsay, IN2P3-CNRS, Université Paris Sud, Orsay, France Department of Physics, University of the Western Cape, Bellville 7535, South Africa Institute für Kernphysik, Universität zu Köln, 50937 Köln, Germany

I. Poltoratska, P. von Neumann-Cosel, ∗ A. Tamii, T. Adachi, 4 C. A. Bertulani, J. Carter, M. Dozono, H. Fujita, K. Fujita, Y. Fujita, K. Hatanaka, M. Itoh, T. Kawabata, Y. Kalmykov, A. M. Krumbholz, E. Litvinova, H. Matsubara, K. Nakanishi, R. Neveling, H. Okamura, H. J. Ong, B. Özel-Tashenov, V. Yu. Ponomarev, A. Richter, 14 B. Rubio, H. Sakaguchi, Y. Sakemi, Y. Sasamoto, Y. Shimbara, 16 Y. Shimizu, F. D. Smit, T. Suzuki, Y. Tameshige, J. Wambach, M. Yosoi, and J. Zenihiro Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan Kernfysisch Versneller Instituut, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa Department of Physics, Kyushu University, Fukuoka 812-8581, Japan Cyclotron and Radioisotope Center, Tohoku University, Sendai, 980-8578, Japan Department of Physics, Kyoto University, Kyoto 606-8502, Japan ExtreMe Matter Institute EMMI and Research Division, GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany Center for Nuclear Study, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan iThemba LABS, Somerset West 7129, South Africa GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany ECT*, Villa Tambosi, I-38123, Villazzano (Trento), Italy Instituto de Fisica Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain Department of Physics, Niigata University, Niigata 950-2102, Japan RIKEN Nishina Center, Wako, Saitama 351-0198, Japan National Institute of Radiological Sciences, Chiba 263-8555, Japan (Dated: January 10, 2021)

The isobaric nuclei 20Ne and 20F were investigated with the 22Ne(p,t)20Ne and 22Ne(p,3He)20F reactions using a beam of protons at Ep = 80 MeV. The former reaction was employed to confirm a tentative candidate for the 5-alpha cluster state in 20Ne, while the latter was used to look for T = 2 isobaric analogue partner states in 20F to states which were already observed above Ex = 20 MeV in 20Ne. The existence of a state which could be considered as a candidate for the 5-alpha cluster state is confirmed here as well as the T = 2 IAS states in 20Ne.

L. M. Donaldson ,1,2,* J. Carter,2 P. von Neumann-Cosel,3 V. O. Nesterenko,4 R. Neveling,1 P.-G. Reinhard,5 I. T. Usman,2 P. Adsley,1,2,6 C. A. Bertulani,7 J. W. Brümmer,6 E. Z. Buthelezi,1 G. R. J. Cooper,8 R. W. Fearick,9 S. V. Förtsch,1 H. Fujita,10 Y. Fujita,10 M. Jingo,2 N. Y. Kheswa,1 W. Kleinig,4 C. O. Kureba,2,11 J. Kvasil,12 M. Latif,2 K. C. W. Li,6 J. P. Mira,1 F. Nemulodi,1 P. Papka,1,6 L. Pellegri,1,2 N. Pietralla,3 V. Yu. Ponomarev,3 B. Rebeiro,13 A. Richter,3 N. Yu. Shirikova,4 E. Sideras-Haddad,2 A. V. Sushkov,4 F. D. Smit,1 G. F. Steyn,1 J. A. Swartz,1,6 and A. Tamii10 1iThemba LABS, Old Faure Road, Faure 7131, South Africa 2School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa 3Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany 4Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia 5Institut für Theoretische Physik II, Universität Erlangen, D-91058 Erlangen, Germany 6Department of Physics, Stellenbosch University, Matieland 7602, South Africa 7Department of Physics and Astronomy, Texas A&M University–Commerce, Commerce, Texas 75429, USA 8School of Geosciences, University of the Witwatersrand, Johannesburg 2050, South Africa 9Department of Physics, University of Cape Town, Rondebosch 7700, South Africa 10Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan 11Department of Physics and Astronomy, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana 12Institute of Particle and Nuclear Physics, Charles University, CZ-18000, Prague 8, Czech Republic 13Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa

Background: Inelastic proton scattering at energies of a few hundred MeV and very-forward scattering angles including 0 degrees has been established as a tool for the study of electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Purpose: Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the isovector giant dipole resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at the iThemba Laboratory for Accelerator Based Sciences in Cape Town, South Africa. The scattering products were momentum-analyzed by the K600 magnetic spectrometer positioned at theta(Lab) = 0 degrees. Using dispersion-matching techniques, energy resolutions of Delta E approximate to 40-50 keV (full width at half maximum) were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photoabsorption cross sections using the equivalent virtual-photon method. Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Results: Fine structure of the IVGDR is observed even for the most deformed nuclei studied. Comparisons between the extracted experimental energy scales and those energy scales obtained from the quasiparticle-phonon model (QPM) and Skyrme separable random phase approximation (SSRPA) predictions provide insight into the role of different giant-resonance damping mechanisms. It can be seen that the scales in the spherical and most likely also in the deformed nuclei mainly result from the fragmentation of the one-particle-one-hole (1p1h) strength into several dominant transitions serving as doorway states. In cases where calculations beyond the 1p1h level are available, some impact of the spreading due to coupling of the two-particle-two-hole (2p2h) states to the 1p1h doorway states is observed. Conclusions: New virtual-photon absorption data for the chain of stable Nd isotopes and 152 5m are presented, with a focus on the phenomenon of nonstatistical cross-section fluctuations, referred to as fine structure, in the energy region of the IVGDR. The wavelet-analysis techniques used allowed for the features of the fine structure to be quantified in the form of characteristic scales. Comparisons between experimental results and model predictions indicate that Landau damping seems to be the main source of the fine structure in both the spherical and deformed nuclei, but calculations including 2p2h degrees of freedom would be beneficial to confirm this for the deformed cases.

Experiments investigating the fine structure of the IsoScalar Giant Monopole Resonance (ISGMR) of 48 Ca were carried out with a 200 MeV alpha inelastic-scattering reaction, using the high energy-resolution capability and the zero-degree setup at the K600 magnetic spectrometer of iThemba LABS, Cape Town, South Africa. Considerable fine structure is observed in the energy region of the ISGMR. Characteristic energy scales are extracted from the experimental data by means of a wavelet analysis and compared with the state-of-the-art theoretical calculations within a Skyrme-RPA (random phase approximation) approach using the finite-rank separable approximation with the inclusion of phonon-phonon coupling (PPC). Good agreement was observed between the experimental data and the theoretical predictions.