The structure of low-lying 1− states in 90,94Zr from (α,α′γ) and (p,p′γ) reactions

The low-lying dipole strength was investigated in 90,94 Zr via the (p,p′γ) reaction at 80 MeV and via the (α,α′γ) reaction at 130 MeV. These experiments were performed at the Research Center for Nuclear Physics (Osaka University) and made combined use of the high-resolution magnetic spectrometer Grand Raiden and the CAGRA HPGe gamma array. The comparison of our results with existing (γ,γ′) reaction data shows differences in the excitation patterns. In the present experimental conditions, in fact, both α and p probes are exciting the investigated 1− states mainly through the short-range nuclear force, expected to favour the population of surface excitations. Distorted Wave Born Approximation (DWBA) calculations were made using form factors built assuming specific transition densities, characterized by a strong neutron component at the nuclear surface and based on Random Phase Approximation (RPA). A combined analysis of the (α,α′γ) and (p,p′γ) data was performed to investigate the isoscalar character of the 1− states in 90,94Zr. Although an overall general consistency was obtained in the studied energy intervals, not all (p,p′γ) cross sections were well reproduced using the isoscalar strength deduced from (α,α′γ) data. This might suggest that the mixing of isoscalar and isovector components and the degree of collectivity are not the same for all the 1− states studied.


Introduction
The Giant Resonances (GRs) strength is effectively described using multipole expansion.An additional classification is imposed on the basis of the isospin symmetry, i.e. each particular multipole strength is further divided in isoscalar or isovector type [1].The isovector electric dipole response of atomic nuclei is dominated by the isovector Giant Dipole Resonance mode (IVGDR, macroscopically interpreted as an oscillation of all neutrons against all protons) [1,2].Ideally, the 100% of the oscillator strength should be associated to the area of a Lorentzian-type curve representing the IVGDR.However, in general, GRs cannot be satisfactorily described just with a single classic damped oscillator response model, since, for example, there is a fine structure and also the strength is not totally associable to the GR mode.Finding hints of systematics in the experimental observations, for a significant fraction of excess strength (i.e.not associated to the IVGDR), is very appealing from a physicist's point of view, because it might suggest the possibility of interpreting a complex nuclear phenomenology in a rather simple way.It can be understood why, following the experimental observation of the systematic presence of excess resonance like structures in the low-energy tail of the IVGDR in neutron-rich nuclei, nuclear physicists started, since the late '60s, to dub this phenomenon as the Pygmy Dipole Resonance (PDR) [3], even without having any detailed theoretical interpretation.In recent years, significant advances in nuclear instrumentation technologies allowed detailed measurements of the low-lying electric dipole strength [4,5,6] and, at the same time, novel advanced theoretical calculations showed the importance of this kind of data, also beyond nuclear structure [7].
This caused a renewed, strong, interest in the study of the PDR phenomenon.A simple macroscopic interpretation of the PDR suggests the existence of a new collective mode originated by the oscillation of the N=Z core of neutron-rich nuclei against the neutron skin, but this is still under debate.It is important to note, however, that the nature of h e p y g m y 1 − states is mixed in terms of isospin.This is already experimentally established [4,8,9,10,11], even though the degree of collectivity of these states is not clarified yet.Interestingly, the importance of the PDR phenomenon is expected to increase right in nuclear systems characterized by extreme conditions of isospin (in exotic neutron-rich nuclei).From the experimental point of view, the importance of u s i n g a multi-messanger approach became clear [12].Indeed, information on the structure of the pygmy states can be effectively extracted by comparing their population cross section obtained with different, complementary probes.Following this view, an experimental campaign was performed at RCNP (Osaka University) featuring a series of experiments in which t h e p y g m y 1 − states were populated in selected target nuclei, using both alpha and proton inelastic scattering as probes.In the following, the results of an experiment of those, studying in particular the 90,94 Zr isotopes, is presented.

Description of the Experiment
Beams of alpha particles and protons, at bombarding energies of 130 MeV and 80 MeV, respectively, were provided by the AVF cyclotron at the RCNP (Osaka University).Inelastically scattered particles were measured by employing the high-resolution spectrometer Grand Raiden [13].In the used forward scattering mode, the Grand Raiden spectrometer was placed at angles of 4.5 and 6.6 degrees, for the alpha and proton beams respectively [14].Highly enriched self-supporting targets of 90,94 Zr with areal densities of 1.95 and 4 mg/cm 2 , respectively, were used.A detailed description of the coincidence setup at the Grand Raiden Spectrometer can be found in Ref. [14].The γ rays emitted following the de-excitation of the studied target nuclei were detected using the 12 HPGe detectors (clover type) of the CAGRA array [15].This was the first time in which a large high-resolution gamma spectrometer was coupled to the Grand Raiden setup.The target nuclei excitation energy was determined through the missing mass method from the measured energies of the scattered beam particles in Grand Raiden.A specific feature of this setup is the possibility of a coincident detection of the scattered beam particles and the γ rays, emitted following the de-excitation of the target nuclei.Ground-state γ-ray transitions from excited states were selected by setting 2D gates corresponding to the loci of points around the diagonal of the Eex vs Eγ matrix (with the condition Eex≈Eγ).The correlation angle between the inelastically scattered particle and the emitted γ rays was also measured for each event.Producing the associated angular correlation plots allowed to identify the multipolarity of the γ transitions.To this aim, experimental data were compared with calculated angular correlation curves, obtained following the prescriptions given in [16].

Data Analysis Results and Interpretation
Inelastic scattering cross sections (α and p) measured in this work for 1 − states in 90 Zr are shown in the left side panels of Fig. 1.For the complete set of results see [17].The counts in the known discrete peaks are indicated with full coloured bars (red and green), while the other grey bars correspond to the total measured counts (including the unresolved strength cross section).The estimated contribution from 1 + states was obtained using the measured M1 strength from [18], this is shown in the grey area with light green bars.The comparison with data from (γ,γ ′ ) reaction measurements ( [19] and [20]) shows that only a fraction of the 1 − states, concentrated in the lower-energy part of the interval, is populated in the present experiments (i.e. when using probes in which the main excitation mechanism is driven by the nuclear force).Similar findings were systematically obtained in past years for other nuclei [4].This fact is an experimental indication that these lower-lying 1 − states have a significant isoscalar character.Moreover, following the procedure presented in [20], we could quantify the fraction of the isoscalar electric dipole Energy Weighted Sum Rule (EWSR) exhausted by the 1 − states.For each pygmy state one expects to obtain, using the above procedure [8], the same value of the isoscalar electric dipole EWSR, independently of the used input cross section data (α or p).Therefore, as a consistency check, the fraction of the isoscalar electric dipole EWSR was deduced by fitting the α scattering data with DWBA calculations and these deduced values were then used to calculate the proton cross section without any further normalisation.This coupled analysis of the two-reaction data gave an overall consistent description, with some significant discrepancies though.The found differences between the two sets of data might suggest that the mixing of isoscalar and isovector components is not the same for all 1 − states below the particle binding energy.and [20]).Lower right panel: specific" pygmy" transition density for 90 Zr, characterized by a strong neutron component at the nuclear surface and based on RPA [17].

Figure 1 .
Figure 1.Left side panels: inelastic scattering cross sections (α and p) measured in this work for 1 − states in 90 Zr.Upper right panel: data from (γ,γ ′ ) reaction measurements ([19]and[20]).Lower right panel: specific" pygmy" transition density for 90 Zr, characterized by a strong neutron component at the nuclear surface and based on RPA[17].