arXiv subjects

Y. Hirabayashi

Publications and source records attributed to Y. Hirabayashi.

At least 19 recordsLinked to original sources

arXiv2025

Secondary bow with ripples in $^{12}$C+$^{12}$C rainbow scattering

We report, {for the first time, the emergence of} a secondary bow with ripples in $^{12}$C+$^{12}$C nuclear rainbow scattering. This finding was achieved by studying the experimental angular distributions in $^{12}$C+$^{12}$C scattering at incident energies $E_L$= 240 and 300 MeV, utilizing an extended double-folding model. This model accurately describes all diagonal and off-diagonal coupling potentials derived from the microscopic wave functions for $^{12}$C. Although the observed angular distributions of rainbow scattering at large angles (approaching $90^\circ$) are complicated by the symmetrization of two identical bosonic nuclei, the Airy minimum, associated with a dynamically generated secondary bow with ripples, is clearly identified at approximately 77$^\circ$ for 240 MeV in the fall-off region of the primary nuclear rainbow. This {finding}, along with previous findings in the $^{16}$O+$^{12}$C and $^{13}$C+$^{12}$C systems, {reinforces} the concept of a secondary bow in nuclear rainbow scattering.

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arXiv2025

Existence of a fourth Airy elephant in the nuclear rainbows for $^{12}$C+$^{12}$C scattering

The number of gross structures in the 90$^\circ$ excitation function for $^{12}$C+$^{12}$C elastic scattering, often called Airy elephants, has been of great interest. These structures are caused by refractive scattering and are separated by Airy minima. Their importance stems from their close relationship to the interaction potential between two $^{12}$C nuclei, which also describes the molecular resonances of the compound system at lower energies. Although a unique deep potential was usually determined from rainbow scattering at higher energies, a puzzling discrepancy persisted: the energy at which the Airy minimum $A1$ crosses 90$^\circ$ was $E_{c.m.}\approx$67 MeV for $^{12}$C+$^{12}$C. This is remarkably low compared to approximately 100 MeV for both the $^{16}$O+$^{12}$C and $^{16}$O+$^{16}$O systems. This question remained unanswered until the discovery of the secondary rainbow in the $^{12}$C+$^{12}$C system. We report for the first time that the highest energy at which the dynamically generated Airy minimum of the secondary rainbow crosses 90$^\circ$ is about 100 MeV. This demonstrates that the fourth Airy elephant exists between the Airy minimum $A1$ of the primary nuclear rainbow and that, $A1^{(S)}$, of the secondary rainbow. The long-standing problem concerning the Airy minima and Airy elephants has finally been resolved after decades of concern by recognizing the existence of a dynamically generated secondary rainbow in $^{12}$C+$^{12}$C scattering.

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arXiv2023

$α$ + $^{92}$Zr cluster structure in $^{96}$Mo

In the evaluation of the half-life of the neutrinoless double-$β$ decay ($0νββ$) of a doubly closed-subshell nucleus $^{96}$Zr, the structure of the nucleus $^{96}$Mo is essentially important. The $α$-clustering aspects of $^{96}$Mo are investigated for the first time. By studying the nuclear rainbows in $α$ scattering from $^{92}$Zr at high energies and the characteristic structure of the excitation functions at the extreme backward angle at the low-energy region, the interaction potential between the $α$ particle and the $^{92}$Zr nucleus is determined well in the double folding model. The validity of the double folding model was reinforced by studying $α$ scattering from neighboring nuclei $^{90}$Zr, $^{91}$Zr, and $^{94}$Zr. The double-folding-model calculations reproduced well all the observed angular distributions over a wide range of incident energies and the characteristic excitation functions. By using the obtained potential the $α$ +$^{92}$Zr cluster structure of $^{96}$Mo is investigated in the spirit of a unified description of scattering and structure. The existence of the second-higher nodal band states with the $α$+ $^{92}$Zr cluster structure, in which two more nodes are excited in the relative motion compared with the ground band, is demonstrated. The calculation reproduces well the ground-band states of $^{96}$Mo in agreement with experiment. The experimental $B(E2)$ value of the transition in the ground band is also reproduced well. The effect of $α$ clustering in $^{96}$Mo on the the half-life of the $0νββ$ double-$β$ decay of $^{96}$Zr is discussed.

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arXiv2017

Existence of inelastic supernumerary nuclear rainbow in $^{16}$O+$^{12}$C scattering

The existence of a supernumerary nuclear rainbow in inelastic scattering is reported. This is done by studying inelastic $^{16}$O scattering from $^{12}$C, exciting the $2^+$ (4.44 MeV) state of $^{12}$C and elastic scattering at the incident energies in the range 124 to 200 MeV, using the coupled channels method. An extended double folding potential is used. This is derived from realistic wave functions for $^{12}$C and $^{16}$O calculated with a microscopic $α$ cluster model and a finite-range density-dependent nucleon-nucleon force. Excitations to the $2^+$ (4.44 MeV), 3$^-$ (9.64 MeV) and $4^+$ (14.08 MeV) states of $^{12}$C, and the $3^-$ (6.13 MeV) and $2^+$ (6.92 MeV) states of $^{16}$O are included in the coupled channels calculations. The emergence of the supernumerary bow is understood by the properties of both the Luneburg-lens-like potential in the internal region and diffuse attraction in the outer region. The existence of a supernumerary rainbow for inelastic scattering in addition to the existence of a dynamically created secondary rainbow and a dynamically refracted primary rainbow for elastic scattering, which are not observed in meteorological rainbows, further deepens the understanding of nuclear rainbows.

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arXiv2016

Evidence for a dynamically refracted primary bow in weakly bound $^9$Be rainbow scattering from $^{16}$O

We present for the first time evidence for the existence of a dynamically refracted primary bow for $^{9}$Be+$^{16}$O scattering. This is demonstrated through the use of coupled channel calculations with an extended double folding potential derived from the density-dependent effective two-body force and precise microscopic cluster wave functions for $^{9}$Be. The calculations reproduce the experimental Airy structure in $^{9}$Be+$^{16}$O scattering well.It is found that coupling of a weakly bound $^{9}$Be nucleus to excited states plays the role of a booster lens, dynamically enhancing the refraction over the {\it static} refraction due to the Luneburg lens mean field potential between the ground states of $^{9}$Be and $^{16}$O.

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arXiv2015

Further evidence for a dynamically generated secondary bow in $^{13}$C+$^{12}$C rainbow scattering

The existence of a secondary bow is confirmed for 13C+12C nuclear rainbow scattering in addition to the 16O+12C system. This is found by studying the experimental angular distribution of 13C+12C scattering at the incident 13C energy $E_L$=250 MeV with an extended double folding (EDF) model that describes all the diagonal and off-diagonal coupling potentials derived from the microscopic wave functions for 12C using a density-dependent nucleon-nucleon force. The Airy minimum at θ$ $\approx$70$^\circ$, which is not reproduced by a conventional folding potential, is revealed to be a secondary bow generated dynamically by a coupling to the excited state 2+ (4.44 MeV) of 12C. The essential importance of the quadruple {\it Y2} term (reorientation term) of potential of the excited state 2+ of 12C for the emergence of a secondary bow is found. The mechanism of the secondary bow is intuitively explained by showing how the trajectories are refracted dynamically into the classically forbidden angular region beyond the rainbow angle of the primary rainbow.

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arXiv2015

Airy structure in $^{16}$O+$^{14}$C nuclear rainbow scattering

The Airy structure in $^{16}$O+$^{14}$C rainbow scattering is studied with an extended double folding (EDF) model that describes all the diagonal and off-diagonal coupling potentials derived from the microscopic realistic wave functions for $^{16}$O using a density-dependent nucleon-nucleon force. The experimental angular distributions at $E_L$=132, 281 and 382.2 MeV are well reproduced by the calculations. By studying the energy evolution of the Airy structure, the Airy minimum at around $θ$=76$^\circ$ in the angular distribution at $E_L$=132 MeV is assigned as the second order Airy minimum $A2$ in contrast to the recent literature which assigns it as the third order $A3$. The Airy minima in the 90$^\circ$ excitation function is investigated in comparison with well-known $^{16}$O+$^{16}$O and $^{12}$C+$^{12}$C systems. Evolution of the Airy structure into the molecular resonances with the $^{16}$O+$^{14}$C cluster structure in the low energy region around $E_{c.m.}$=30 MeV is discussed. It is predicted theoretically for the first time for a non-$4N$ $^{16}$O+$^{14}$C system that Airy elephants in the 90$^\circ$ excitation function are present.

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arXiv2015

Emergence of a secondary rainbow and the dynamical polarization potential for 16O on 12C at 330 MeV

Background: An anomaly in the elastic scattering of O-16 on C-12 around 300 MeV was resolved by including collective excitations of both nuclei, leading to a secondary rainbow. There is little systematic knowledge of the contribution of collective excitations to the interaction between nuclei, particularly in the overlap region of heavy nuclei. Purpose: To study the dynamic polarization potential (DPP) generated by channel coupling that had been validated for a case where scattering is sensitive to the nuclear potential over a wide radial range; to exhibit evidence of the non-locality due to collective coupling; to validate, or otherwise, the representation of DPPs by uniform renormalization of potentials. Methods: S-matrix to potential inversion yields local potentials reproducing the elastic channel S-matrix of coupled channel calculations. Subtracting the elastic channel uncoupled potential yields a local L-independent representation of the DPP. The dependence of the DPP on the nature of the coupled states and other parameters can be studied. Results: Local DPPs were found due to the excitation of C-12 and the combined excitation of O-16 and C-12. The radial forms found were very different from uniform renormalization of the potential. Full coupling led to a 10 percent increase in the volume integral of the real potential. Evidence for the non-locality of the underlying formal DPP and the effect of direct coupling between the collective states is found. Conclusions: The local DPP generating the secondary rainbow is found. DPPs have forms depending on the specific excitations and cannot be represented by a uniform renormalization of the potential. The method is useful for study of the contribution of collective excitations to internuclear potentials, concerning which remarkably little is known in general.

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arXiv2014

Refractive effects and Airy structure in inelastic $^{16}$O+$^{12}$C rainbow scattering

Inelastic $^{16}$O +$^{12}$C rainbow scattering to the $2^+$ (4.44 MeV) state of $^{12}$C was measured at the incident energies, $E_L$ = 170, 181, 200, 260 and 281 MeV. A systematic analysis of the experimental angular distributions was performed using the coupled channels method with an extended double folding potential derived from realistic wave functions for $^{12}$C and $^{16}$O calculated with a microscopic $α$ cluster model and a finite-range density-dependent nucleon-nucleon force.The coupled channels analysis of the measured inelastic scattering data shows consistently some Airy-like structure in the inelastic scattering cross sections for the first $2^+$ state of $^{12}$C, which is somewhat obscured and still not clearly visible in the measured data. The Airy minimum was identified from the analysis and the systematic energy evolution of the Airy structure was studied. The Airy minimum in inelastic scattering is found to be shifted backward compared with that in elastic scattering.

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arXiv2014

Similarity between nuclear rainbow and meteorological rainbow -- evidence for nuclear ripples

We present evidence for the nuclear ripples superimposed on the Airy structure of the nuclear rainbow, which is similar to the meteorological rainbow. The mechanism of the nuclear ripples is also similar to that of the meteorological rainbow, which is caused by the interference between the externally reflective waves and refractive waves. The nuclear ripple structure was confirmed by analyzing the elastic angular distribution in $^{16}$O+$^{12}$C rainbow scattering at $E_L$=115.9 MeV using the coupled channels method by taking account of coupling to the excited states of $^{12}$C and $^{16}$O with a double folding model derived from a density-dependent effective nucleon-nucleon force with realistic wave functions for $^{12}$C and $^{16}$O. The coupling to the excited states plays the role of creating the external reflection.

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arXiv2014

Evidence for a secondary bow in Newton's zero-order nuclear rainbow

Rainbows are generally considered to be caused by static refraction and reflection. A primary and a secondary rainbow appear due to refraction and internal reflection in a raindrop as explained by Newton. The quantum nuclear rainbow, which is generated by refraction in the nucleus droplet, only has a "primary" rainbow. Here we show for the first time evidence for the existence of a secondary nuclear rainbow generated dynamically by coupling to an excited state without internal reflection. This has been demonstrated for experimental $^{16}$O+$^{12}$C scattering using the coupled channel method with an extended double folding potential derived from microscopic realistic wave functions for $^{12}$C and $^{16}$O.

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arXiv2013

Unification of Airy structure in inelastic $α$ +$^{16}$O scattering and $α$-cluster structure with core excitation in $^{20}$Ne

The Airy structure of the nuclear rainbow and prerainbow in inelastic and elastic $α+^{16}$O scattering is studied with the coupled channel method using a folding potential derived from the microscopic wave functions of $^{16}$O. The theoretical calculations reproduce the characteristic energy evolution of the Airy minimum of the experimental angular distributions. The energy levels with $α$-cluster structure in $^{20}$Ne are reproduced well using the potentials determined from the analysis of scattering. It is shown that the emergence of the $K=0_3^+$ $α$-cluster band with core excitation at 7.19 MeV in $^{20}$Ne is intimately related to the emergence of the prerainbow and rainbow in inelastic scattering to the $^{16}$O($0^+_2$). It is found that the $α$-cluster states with core excitation, the prerainbow and the rainbow in inelastic scattering are understood in a unified way as well as in the case of elastic scattering.

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arXiv2013

Observation of Airy minimum in elastic and inelastic scattering of $^3$He from $^{12}$C at 50.5 and 60 MeV and alpha particle condensation in $^{12}$C

Angular distributions for elastic and inelastic scattering of $^3$He from $^{12}$C were measured at energies 50.5 and 60 MeV. The Airy minimum of the prerainbow scattering was clearly observed in the angular distributions for the 0$_2^+$ (7.65 MeV) state of $^{12}$C (Hoyle state). The experimental results were analyzed with a coupled channels method with double folding potentials derived from the microscopic wave functions for the ground 0$_1^+$, 2$^+$ (4.44 MeV), 3$^-$ (9.64 MeV) and 0$_2^+$ states. The analysis supports the view that the Hoyle state is a three alpha particle condensate with a large radius of dilute matter distribution.

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arXiv2011

Systematic description of 6Li(n, n')6Li* $\to$ d + $α$ reactions with the microscopic coupled-channels method

We investigate $^6$Li($n$, $n'$)$^6$Li$^*$ $\to$ $d$ + $α$ reactions by using the continuum-discretized coupled-channels method with the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction. In this study, the $^6$Li nucleus is described as a $d$ + $α$ cluster model. The calculated elastic cross sections for incident energies between 7.47 and 24.0 MeV are good agreement with experimental data. Furthermore, we show the neutron spectra to $^6$Li breakup states measured at selected angular points and incident energies can be also reproduced systematically.

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arXiv2011

Prerainbow Oscillations in $^3$He Scattering from the Hoyle State of $^{12}$c and Alpha Particle Condensation

$^3$He+$^{12}$C scattering is studied in a coupled channel method by using a double folding model with microscopic wave functions of $^{12}$C. Experimental angular distributions in elastic and inelastic scattering to the $2^+$ (4.44 MeV), 0$^+_2$ (7.65 MeV) and 3$^-$ (9.63 MeV) states of $^{12}$C are well reproduced. It is found that the Airy minimum of the prerainbow oscillations for the Hoyle state is considerably shifted to a larger angle due to its dilute density distribution compared with that of the normal ground state in agreement with the idea of $α$ particle condensation.

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arXiv2011

Evidence for higher nodal band states with $^3$He cluster structure in $^{19}$Ne and prerainbows in $^3$He+$^{16}$O scattering

The existence of a higher nodal band state with a $^{3}$He cluster structure, i.e. a vibrational mode in which the inter-cluster relative motion is excited, in $^{19}$Ne in addition to those with the $α$ cluster structure in $^{20}$Ne and the $^{16}$O cluster structure in $^{32}$S, is suggested, which reinforces the importance of the concept of $^3$He-clustering in nuclei. This conclusion was reached by investigating $^{3}$He scattering from $^{16}$O in a wide range of incident energies and prerainbow oscillations.

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arXiv2011

$α$-particle condensate states in $^{16}$O

The existence of a rotational band with the $α$+$^{12}$C($0_2^+$) cluster structure, in which three $α$ particles in $^{12}$C($0_2^+$) are locally condensed, is demonstrated near the four-$α$ threshold of $^{16}$O in agreement with experiment. This is achieved by studying structure and scattering for the $α$+$^{12}$C($0_2^+$) system in a unified way. A drastic reduction (quenching) of the moment of the inertia of the $0^+$ state at 15.1 MeV just above the four-$α$ threshold in $^{16}$O suggests that it could be a candidate for the superfluid state in $α$-particle condensation.

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arXiv2011

Evidence for strong refraction of $^3$He in an alpha-particle condensate

We have analyzed $^{3}$He scattering from $^{12}$C at 34.7 and 72 MeV in a coupled channel method with a double folding potential derived from the precise wave functions for the ground 0$^+$ state and $0_2^+$ (7.65 MeV) Hoyle state, which has been suggested to be an $α$ particle condensate. It is found that strong refraction of $^3$He in the Hoyle state can be clearly seen in the experimental angular distribution at {\it low} incident energy region as an Airy minimum of the {\it pre-rainbow oscillations}.

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