Determination of nuclear radii for unstable states in C 12 with diffraction inelastic scattering

Abstract. α + 12 C elastic and inelastic to the Hoyle state (0 + 2 , 7.65 MeV) differential cross-sections were measured at the energies 60 and 65 MeV with the aim of testing the microscopic wave function [1] widely used in modern structure calculations of 12 C. Deep rainbow (Airy) minima were observed in all four curves. The minima in the inelastic angular distributions are shifted to the larger angles relatively those in the elastic ones, which testify the radius enhancement of the Hoyle state. In general, the DWBA calculations failed to reproduce the details of the cross sections in the region of the rainbow minima in the inelastic scattering data. However, by using the phenomenological density with rms radius equal 2.9 fm, we can reproduce the Airy minimum positions.

Section: The Inelastic Form Factor Was Taken In the Form: V If (R) supporting

confidence: 66%

“…The microscopic wave function calculated by Kamimura [1] represents the basis of different theoretical approaches to the problem. However, some predictions made by using this wave function, e.g., the radius of the Hoyle state, were not confirmed by empirical data [2]. Thus additional tests are highly desirable.…”

Section: Introduction and Experimental Datamentioning

confidence: 99%

Study of the structure of the Hoyle state by refractive α-scattering

Goncharov

Demyanova

Gloukhov

et al. 2014

“…Most of the other cluster models like the antisymmetrized molecular dynamics (AMD) also predicted the enhancement of the radius of the Hoyle state, though in a less extent. The experimental data on the inelastic scattering [2] supported these suggestions (the collection of the theoretical radii values together with the experimental one is given in Table.1). Moreover, another prediction of the APC that all three alpha particles in 12 C should predominantly occupy the lowest s-orbit also was confirmed by experiment giving for the occupation probability W s (α) = 0.6 [3] (to be compared with the theoretical value 0.7 -0.8 [4]).…”

Section: Introductionsupporting

confidence: 59%

“…The Modified diffraction model (MDM) [2] was used for estimating the radii of the 14.08 and 13.75 MeV states. The best fit was obtained with the diffraction radius of the transition to the 14.08 MeV state R dif = 4.2 fm (left parts of Fig.2, 3), which is almost 1 fm less than that for the elastic scattering.…”

Section: Resultsmentioning

confidence: 99%

Rotational band in¹²C based on the Hoyle state

Ogloblin

Demyanova

Danilov

et al. 2014

Abstract. α + 12 C inelastic differential cross-sections were measured at the energies 65 and 110 MeV. A new broad state at 13.75 MeV was observed. Its spin-parity has been determined as 4 + and the diffraction radius of the corresponding L = 4 transition is ~ 0.8 fm larger than that of the excitation of the 4+, 14.8 MeV level. The 13.75 MeV state was considered to be the third member of the rotational band based on the Hoyle state.

“…Our result is close to the prediction of the Fermionic Molecular Dynamic (FMD) model (3.48 fm) [4], but it is considerably larger than predicted by the ab-initio Lattice Effective Field Theory (EFT) (2.4 fm) [8] and smaller than predicted by the "BEC-like" model (3.83 fm) [5]. It is slightly larger than the one extracted (2.89(4) fm) from 12 C(p, p ) data [22]. A third 2 + state above 11 MeV cannot be excluded by our data but a further study at higher energy is required to confirm the hint of a third 2 + state observed in this study.…”

Section: Resultsmentioning

confidence: 56%

The structure of the Hoyle state and its 2⁺partner state in¹²C

Gai

2012

Abstract. We have measured the 12 C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO 2 (80%) + N 2 (20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. We measured complete angular distributions (between 9.1 -10.7 MeV) from which we determine the cross section yield curve and E1 − E2 relative phases leading to an unambiguous identification of the second 2 + state in 12 C at 10.03(11) MeV. The observed spectrum of 12 C below 12 MeV including the 2 + 2 state observed in this work resembles the rotation-vibration spectrum predicted for a triangular shape oblate spinning top in which the Hoyle state is the first vibrational breathing mode of the triangular three alpha-particle system. We also observed a hint of the 2 + 3 state which is predicted by the U(7) model as a member of the 1 − bending mode band, but the existence of this 2 + 3 is yet to be confirmed. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D 3h symmetry) allows us to compare the moment of inertia of the predicted Hoyle rotational band to the ground state rotational band and in this way extract the (large) rms radius of the Hoyle state of 3.22(8) fm. We compare the deduced rms radius with recent ab-initio theories and cluster models as well as the radius extracted from 12 C(p, p ) data.