Study of the isospin character of 1-states using hadronic probes at intermediate energies

The complementary (γ,γ′) and (α,α′γ) reactions were used to study the isospin properties of lowlying E1 excitations in the doubly-magic nucleus 48Ca. In contrast to heavier nuclei, a state-to-state change in isospin character was revealed in 48Ca and a dominant isoscalar excitation was found which is interpreted as an isoscalar oscillation. Recently, protons at 80 MeV were used as an additional hadronic probe in a p-γ coincidence experiment on 140Ce for the first time. Results of the experiments on 48Ca and first results of the 140Ce will be presented in this contribution.


Introduction
Low-lying electric dipole excitations, in particular the electric Pygmy Dipole Resonance (PDR), were investigated in neutron-rich nuclei using various experimental methods [1].Aiming at isospin characters of these 1 − states, it has been demonstrated that the complementary studies of real-photon scattering and high-resolution (α, α γ) coincidence experiments at 136 MeV allow separating isovector and isoscalar dipole response which is important for a deeper understanding of the underlying mechanisms generating the dipole strength [2].Systematic studies using these complementary probes revealed a splitting into low-lying isospin-mixed E1 excitations and higher-lying dominantly isovector E1 excitations in neutron-magic, proton-magic, and non-magic nuclei (namely 140 Ce, 138 Ba, 124 Sn, and 94 Mo) [2][3][4][5].This experimentally observed common feature of the low-lying E1 response is reproduced by several theoretical calculations (see, e.g., Refs.[6][7][8][9]) which suggest a distinction between a low-lying neutron-skin oscillation mode and a transitional mode towards the well-known isovector Giant Dipole Resonance (IVGDR) [10].Recently, the crossover between the neutron-skin mode and the higherlying proton-neutron oscillation mode was investigated in detail by means of random-phase approximation (RPA) calculations [11] and a decomposition method was introduced which might be important for a robust comparison with experimental data.In addition to the aforementioned α-particles, the hadronic probe of 17 O at 20 MeV/u was recently used in a high-resolution experiment on 208 Pb at Legnaro National Laboratory [12].a e-mail: derya@ikp.uni-koeln.de In the following, we present results of two experiments using the hadronic probes of α particles at 136 MeV and protons at 80 MeV which we performed to achieve a better understanding of the nature of low-lying E1 excitations in 48 Ca and 140 Ce.The 48 Ca(α, α γ) and 140 Ce(p, p γ) experiments go beyond the systematic study of low-lying dipole excitations in (α, α γ) and (γ, γ ) experiments in two ways: On the one hand, by studying a much lighter neutron-rich nucleus and, on the other hand, by using a complementary hadronic probe with a higher energy per nucleon, namely protons at 80 MeV which penetrate more deeply into the nucleus.

Experimental setup and results
Both experiments were performed at the KVI Groningen, The Netherlands, exploiting the Big-Bite Spectrometer in combination with an array of HPGe detectors for γ spectroscopy.The scattered particles and the de-exciting γrays were acquired in hardware coincidence.In the dataanalysis process, particle-γ coincidence matrices are constructed which are then used to generate energy spectra with specific energy conditions on the excitation energy (E x ) and the γ-ray energy (E γ ).Gates on ground-state transitions (E x = E γ ) highly increase the sensitivity to dipole transitions which dominantly decay via this channel.Details on the experimental setup and data analysis tools can be found in Ref. [13] The strong isoscalar state is interpreted as a pure isoscalar oscillation on basis of RPA calculations [16] under consideration of the corresponding velocity fields and transition densities.Furthermore, the well-separated dominant isovector and isoscalar states at 7.3 MeV and 7.6 MeV, respectively, are an optimal test case for the investigation of isospin mixing in a two-state mixing approach.A value of 0.061 (6) was determined for the squared mixing amplitude.This results in an isospin-mixing matrix element of 85(3) keV.Further results of this experiment were presented in more detail in Ref. [17].
Figure 1.Cross sections obtained in the 48 Ca(α, α γ) experiment (upper panel) in comparison with results of a real-photon scattering experiment [14] (lower panel).

Results of the 140 Ce(p, p γ) experiment
The neutron-magic 140 Ce was the first nucleus for which an isospin splitting of low-lying E1 excitations was observed and it is the first nucleus for which the studies were extended by a (p, p γ) experiment at intermediate energy.The summed γ-ray spectrum of all HPGe detectors with a gate on ground-state transitions obtained in the 140 Ce(p, p γ) experiment is shown in Fig. 2. Dipole transitions were identified via their groundstate transition energy in comparison with (γ, γ ) data [18,19].Singles proton-scattering cross sections were determined on basis of this spectrum.Compared to the results from the inelastic α-scattering experiment, the proton-scattering cross sections are almost one order of magnitude smaller.The ratio of the cross sections is shown in Fig. 2. It is nearly constant with an average value of (dσ/dΩ α )/(dσ/dΩ p ) = 6.2 (7).The central part of the nucleon-nucleon interaction is strongly energydependent [20] and decreases with increasing energy from 34 MeV/u to 80 MeV/u.This also leads to a higher degree of transparency for the proton probe and additional cancellation effects for dipole transitions.The experimentally determined ratio for the cross sections is reproduced by Distorted-Wave Born Approximation (DWBA) calculations.

Summary and outlook
Inelastic scattering experiments using hadronic probes at intermediate energies, namely an (α, α γ) experiment at E α = 136 MeV on the doubly-magic 48 Ca and a (p, p γ) experiment at E p = 80 MeV on the neutron-magic 140 Ce were performed at KVI Groningen to further study the nature of low-lying E1 strength.These experiments complement previous real-photon scattering experiments on both nuclei [14,18] and an additional 140 Ce(α, α γ) experiment [2].In contrast to the observations in heavier nuclei, lowlying E1 excitations in the lighter nucleus 48 Ca show a state-to-state dependent isospin character.Furthermore, a strong isoscalar dipole state was revealed which supports theoretical predictions of a strong isoscalar oscillation [16].
For the dipole excitations in 140 Ce, the singles protonscattering cross sections are considerably smaller compared to the α-scattering cross sections.Nevertheless, the general excitation pattern seems to be very similar which is supported by a nearly constant ratio of these cross sections.
In the future, different experimental techniques will be combined to achieve a deeper understanding of coexisting electric dipole modes throughout the nuclear landscape.Essential observables testing the underlying structures more thoroughly include γ-decay branchings, isospin characters, as well as single-particle contents.In particular, the isospin character of 1 − states will be addressed in particle-γ coincidence experiments with hadronic probes at intermediate energies at iThemba LABS in Somerset West, South Africa, and within an experimental PDR campaign with the CAGRA Clover-detector array at RCNP in Osaka, Japan.

Figure 2 .
Figure 2. Summed γ-ray spectrum of all HPGe detectors with gate on E x = E γ measured in the 140 Ce(p, p γ) experiment.Dipole transitions are marked with stars.

Figure 3 .
Figure 3. Ratios of singles α-scattering cross sections [2] and proton-scattering cross sections (this work) for the dipole excitations observed in both experiments.The horizontal line indicates the average ratio.

Table 2 .
. Results of the two experiments on 48 Ca and 140 Ce are presented in the following subsections.Main experimental parameters are given in DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2015

Table 1 .
[14]15]ental parameters for the 48 Ca(α, α γ) and 140 Ce(p, p γ) experiments.Low-lying E1 excitations and their B(E1) strength distributions in stable Ca isotopes, including the doublymagic48Ca, have been studied in several (γ, γ ) experiments[14,15].Hence, the results of the 48 Ca(α, α γ) experiment of this work, allow a comparison of singles α-scattering cross sections and reduced B(E1)↑ transition strengths[14](presented in Fig.1) which gives access to the isospin character of low-lying 1 − states in 48 Ca.It reveals a state-to-state dependent isospin character of the 1 − states where isoscalar, isospin-mixed, and isovector dipole excitations are in close vicinity.An isospin splitting as observed in the heavier nuclei is not present in 48 Ca.
Remarkable is also a strong dominantly isoscalar state at 7.6 MeV close to a strong isovector state at 7.3 MeV.