A. N. Danilov

Observation of abnormally large radii of nuclei in excited states in the vicinity of neutron thresholds

Differential cross sections for inelastic scattering leading to the excitation of some nuclear states situated near neutron-emission thresholds were analyzed. With the aid of a modified diffraction model, abnormally large radii were found for the 1/21+ state of the 13C nucleus at 3.09 MeV, for the first levels of positive-parity rotational bands in the 9Be (1/2+ level at 1.68 MeV and 5/2+ level at 3.05 MeV) and 11Be (5/2+ level at 1.78 MeV and 3/2+ level at 3.41 MeV) nuclei, and for the 21+ state of the 14Be nucleus at 1.54 MeV and 11− state of the 12Be nucleus at 2.7 MeV. All of these states possess signatures typical of neutron halos.

α + 12C scattering at 110 MeV: Has exotic 7.65 MeV Hoyle’s state signatures “alpha-condensate” structure?

We present new measurements of the α + 12C elastic and inelastic (to the states 4.44, 7.65, and 9.64 MeV) scattering at Elab = 110 MeV in the wide angular range from ∼10° to 175°, which enable us to examine the condensate and cluster properties of the low-lying excited states in 12C. We present the diffraction-radius analysis of our data together with a considerable amount of the existing data. The magnitudes of the diffraction radii for the ground and the first excited (4.44 MeV) states are found to be equal, whereas they appear to be enhanced by ∼0.6 fm both for 7.65 and 9.64 MeV states. This result shows that the radius of the Hoyle’s 02+, 7.65 MeV state in 12C is by a factor of ∼1.2–1.3 larger than that of the ground state. It is demonstrated that the direct transfer mechanism of 8Be dominates at the largest angles in all four reactions reported here. The configuration corresponding to the transfer of 8Be in its ground state (Iπ = 0+) with L = 0 turns out to be the most important for the 7.65 MeV state of 12C. Evidence of existence of some features of α-condensed structure of the Hoyle’s 02+ state in 12C was obtained: its enhanced radius and large contribution of α-particle configuration with L = 0.

Study of rlastic and inelastic 11B +α scattering and search for cluster states of enlarged radius in 11B

The differential cross sections for elastic and inelastic 11B + α scattering were measured at the alpha-particle energy of 65 MeV, the inelastic-scattering processes leading to the excitation of known states of 11B up to excitation energies of about 14 MeV. Data on elastic scattering were analyzed together with those that were published earlier for lower energies. The cross sections for inelastic scattering were analyzed on the basis of the distorted-wave method. A modified diffractionmodel was used to determine the root-mean-square radii of excited states. The radii of states whose excitation energies were below about 7MeV were found to agree with radius of the ground state to within 0.1 to 0.15 fm. This result complieswith the traditional idea that the low-lying states of 11B have a shell structure. The possibility that these states belong to the predicted rotational bands, which, if any, are truncated to three states, cannot be ruled out either. The majority of the observed highly excited states are distributed among four rotational bands. The moments of inertia of these bands are close; for the band based on the 3/2− state at E* = 8.56 MeV, they are even higher than those of the Hoyle state in the 12C nucleus. The measured radii of states associated with these bands of 11B are larger than the ground-state radius by 0.7 to 1.0 fm and are also close to the radius of the Hoyle state. The results of the present study agree with the existing predictions that the cluster structure of the 11B nucleus is diverse at high excitation energies. The hypothesis that the 11B nucleus features a “giant” state of size commensurate with those in heavy nuclei was not confirmed.

Neutron Halo in the Exotic First Excited State of 9Be

Differential cross sections for elastic and inelastic 9Be + α scattering (the inelastic scattering leading to the 1.68- and 2.43-MeV states) were measured at the energies of 40 and 90 MeV. The radii of the excited states in question were determined on the basis of a modified diffraction model. The root-mean-square radius of the level at 1.68 MeV proved to be approximately 1 fm larger than the radii of both neighboring states. The reason is that, for this level, there is a neutron halo whose properties are similar to the properties of the known halo in the 11Be nucleus. This result is the first observation of a halo in an unbound state lying above the neutronemission threshold.

Nuclear states with anomalously large radius (size isomers)

Methods of determination of the nuclear excited state radii are discussed together with the recently obtained data on the states of some light nuclei having abnormally large radii (size isomers). It is shown that such states include excited neutron-halo states in 9Be, 11Be, and 13C and some alpha-cluster states in 12C, 11B, and 13C. Among the latter ones, there is the well-known Hoyle state in 12C—the structure of this state exhibit rudimentary features of alpha-particle states.

Analogues of the exotic Hoyle state in the 12C nucleus

Experimental data on inelastic scattering of alpha particles by the 11B, 12C, and 13C nuclei are analyzed using the modified diffraction model and the radii of these nuclei in some “abnormal” excited states are found. It is shown that the 02+ (7.65 MeV) Hoyle state in the 12C nucleus is the base state for a new 02+–22+–42+ rotational band (in addition to the ground-state band), in which the third member is the discovered 42+ (13.75 MeV) state. The radii of the 12C nucleus in the above-mentioned three states are 25–30% larger than its ground state radius. It is found that the radii of the 1/2– (8.86 MeV) state in the 13C nucleus and the 3/2– (8.56 MeV) state in the 11B nucleus are close to the radius of the Hoyle state in 12C and that a similar rotational band is based on the 8.56 MeV state. The above 13C and 11B states can be regarded as analogues of the Hoyle state. The prediction of the alpha-condensation model that a similar analogue in 11B is the 12.56 MeV state with a radius that is comparable with the nuclear radius of uranium was not confirmed.

Nuclear Threshold States: Yesterday, Today, Tomorrow

50 years ago exotic nuclear states with abnormally large radii located close to the thresholds of emission of nucleons or clusters were predicted. Recently a hypothesis of possible existence of α‐particle Bose condensation was proposed. The 02+(7.65 MeV) state of 12C (so‐called Hoyle state) is considered to be the prototype of such condensed state and have a dilute structure. We propose two methods for searching the α‐condensate signatures in the Hoyle state and some other ones near the α‐thresholds by using inelastic diffractive and rainbow scattering. Inelastic scattering of 2H, 3He, 4He, 6Li, and 12C on 12C was studied and the enhancement of the 12C radius in the Hoyle state relatively the ground state radius by a factor of 1.2 was demonstrated. Another signature of the condensate structure, 70% probability of all three α‐particles to be in the s‐state, was observed for the Hoyle state by studying the 8Be transfer reaction. The analogs of the Hoyle state with enhanced radii were identified in 11B and 1...

Proton halo in the 13 N nucleus

We demonstrate that the radii of excited nuclear states can be estimated using the (3He, t) charge-exchange reaction and relying on the modified diffraction model. The radius of the N excited state with an excitation energy of E*=2.73 MeV, which lies in a continuous spectrum, is determined. The radius of this state proves to be close to that of the mirror 3.09-MeV state of the 13С nucleus, which possesses a neutron halo but lies in a discrete spectrum. Thereby, we demonstrate that the 2.37-MeV state of the 13N nucleus has a proton halo. The analysis is based on published measurements of differential cross sections for relevant reactions.

Use of (3He, t) charge-exchange reactions in determining radii of excited states of nuclei

A method for determining the radii of excited states of nuclei by means of (3He, t) charge-exchange reactions was proposed. Two versions of a comparison of differential cross sections for (3He, t) reactions were considered. The first relies on a comparison with cross sections for inelastic-scattering processes leading to the formation of isobaric analog states, while the second involves (3He, t) reactions leading to the production of the ground state. The two versions in question yield similar results and make it possible to determine the radius of the first excited state of the 13N nucleus. This state has the excitation energy of E* = 2.37 MeV, lying above the proton-emission threshold. The resulting radius proved to be enhanced in relation to the ground state and is close to the radius of the 3.09-MeV isobaric analog state of the 13С nucleus, which has a neutron halo. This permitted drawing the conclusion that the 13N nucleus in the 2.37-MeV state has a proton halo. The possibility of revealing a proton halo in other states of light nuclei is considered.

Role of 8Be heavy stripping mechanism in the α + 12C inelastic scattering to the near-3α-threshold states in 12C

The angular distributions of α + 12C elastic and inelastic (to the 4.44 MeV, 2+; 7.65MeV, 0+; and 9.64MeV, 3− states) scattering at 110 MeV are characterized by pronounced enhancement and strong oscillations at large angles. We performed calculations of the differential cross sections of these reactions assuming a potential scattering in the forward hemisphere and the direct transfer of 8Be cluster θc.m. > 90°. We showed that the α + 8Be cluster configuration with relative angular momentum L = 0 dominates in the Hoyle state being 4.4 times larger than that in the ground state. This result also contributes to the verification of αBEC hypothesis and is consistent with the conjecture of a dilute 3α structure of the Hoyle state. In the 9.64 MeV, 3− state, a positive interference of all allowed α + 8Be configurations with a dominance of the p-orbital (49%) α-8Be relative motion is found. This finding manifests the exotic 3α, but hardly condensed structure of the 9.64-MeV 3− state in 12C.