Nuclear giant resonances (GRs) are highly collective excitations in atomic nuclei, where a significant fraction of nucleons (protons and neutrons) oscillate coherently. These resonances provide valuable insights into nuclear structure and are commonly interpreted as excitations of phonons, essentially meaning quantized vibration modes with corresponding quantum numbers.

GRs usually emerge as excitations from the ground state, but GRs built on already excited states are also possible, and those built on other GRs are called multiphonon states. The double Gamow–Teller giant resonance (DGTGR) is one such two-phonon state, where a Gamow–Teller GR is built on another Gamow–Teller GR. Proposed in 1989 by Auerbach, Zamick, and Zheng, DGTGR is characterized by the double Gamow–Teller (DGT) operator ()², where  represents the spin operator and () represents the isospin raising or lowering operator.

The study of DGTGR is important to the understanding of the nuclear collective excitations, as well as the understanding of the double beta decay, in which a major transition is through the DGT operator. However, DGTGR is challenging to observe experimentally due to the stringent conditions required for its detection. The probe used in the experiment must induce double isospin-flip transitions, which requires a reaction such that the target nucleus undergoes replacement of two neutrons with two protons or vice versa. Also, the spins of these two nucleons should be both flipped from the requirement of double spin-flip. Additionally, the incident energy should be high (≳ 100 MeV/nucleon) to ensure the dominance of direct reactions and reliable reaction theories.

In this study, we utilized a double charge exchange (DCX) reaction of (¹²C, ¹²Be() with an incident energy of 250 MeV/nucleon because it satisfies all these conditions. When bombarded on a target nucleus with a ¹²C beam, DCX reaction occurs, in which two protons in ¹²C are replaced by two neutrons in the target nucleus, transforming it into ¹²Be.

During this reaction, the ground state of ¹²C, which has a spin-parity of 0⁺, undergoes a double spin-flip transition via the intermediate state of ¹²Be (g.s., 1⁺), leading to the formation of the excited state ¹²Be(). Thus, the double isospin- and spin-flip process in the target is enhanced with this probe. An experimental advantage of this probe is that the final state ¹²Be()decays into the ground state with emitting an e⁺e^– pair and can be identified by detecting the 511-keV γ-ray resulting from the annihilation of the e⁺.

We used ⁴⁸Ca as the first target nucleus for our DGTGR study. With 20 protons and 28 neutrons, ⁴⁸Ca is a doubly magic nucleus. It somewhat simplifies the theoretical description of the target, allowing precise studies. Another important feature of ⁴⁸Ca is that it is among the eleven nuclei that decay by double beta decay.

We conducted our experiment at the RI Beam Factory (RIBF) at RIKEN, Japan, using the BigRIPS spectrometer. On bombarding a ⁴⁸Ca target with a ¹²C beam at 250 MeV/nucleon, we successfully detected ¹²Be()tagged with γ-rays produced by its decayThe analysis of the energy and the emission angle of ¹²Be()revealed a forward-peaking nature in the double-differential cross-sections (Figure 1). The integrated cross-section at 0° was determined to be 1.33±0.12 μb/sr in the excitation energy region below 34 MeV in ⁴⁸Ti. Approximately 40% of this cross-section was attributed to DGT transitions, corresponding to a DGT strength of .

Our new measurement has provided the first candidate for DGTGR of ⁴⁸Ca, offering new insights into nuclear excitations and their potential application in studies of double beta decay, including that of the nuclear matrix element of neutrinoless double beta decay.

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