Α-particle Condensation Research Articles

Nuclear α-particle Condensation and Dynamics of Cluster Formation

Nuclear α-particle Condensation and Dynamics of Cluster Formation

Active Target for α-Particle Condensation Studies in 16O

An active target has been developed for studying the Hoyle like states in 16O. It is a position and time sensitive detector system based on the Low-Pressure Multy-Wire Proportional Chamber (LPMWPC) technique and Si detectors. The few Torr pressure of methyl ((OCH3)2CH2) serves as a working gas for the LPMWPC operation, and the oxygen atoms of the methyl molecules serve as an experimental target. The main advantage of this new target-detector system is a high sensitivity to the low-energy, highly ionizing particles, produced after photodisintegration of 16O, and the insensitivity to the γ-rays and low ionizing particles, which allows one to detect only the products of the nuclear reaction, which are studied. The threshold energies for detection of α particles and 12C nuclei are about 50 keV and 100 keV, respectively. Temporal and positional resolution of the LPMWPC modules was investigated with the use of the α-particle source. This paper discusses the architecture of the active target and the test results of the prototype MWPC detector. This installation has been constructed to study the cluster states at 15.1 MeV in 16O using the proton beams from the Yerevan proton cyclotron and the Compton backscattered photon beams of the ELI-NP facility.

Theory for Quartet Condensation in Fermi Systems with Applications to Nuclei and Nuclear Matter

The theory of quartet condensation is further developed. The onset of quartet- ting in homogeneous fermionic matter is studied with the help of an in-medium modified four fermion equation. It is found that at very low density quartetting wins over pairing. At zero temperature, in analogy to pairing, a set of equations for the quartet order parameter is given. Contrary to pairing, quartetting only exists for strong coupling and breaks down for weak coupling. Reasons for this finding are detailed. In an application to nuclear matter, the critical temperature for α particle condensation can reach values up to around 8 MeV. The disappearance of α-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 02+ of 12C is identified as an 'α-particle condensate' state. It is conjectured that such states also exist in heavier na-nuclei, like 16O, 20Ne, etc. The sixth 0+ state in 16O is proposed as an analogue to the Hoyle state. The Gross-Pitaevski equation is employed to make an estimate of the maximum number of a particles a condensate state can contain. Possible quartet condensation in other systems is discussed briefly.

Search for α-particle condensation in nuclei from the Hoyle state deexcitation

Heavy ion reactions induced by few tens MeV/nucleon beams constitute an ideal framework for producing and studying nuclear excited states close to the decay threshold. The fragmentation of quasi-projectiles from the nuclear reaction 40Ca+12C at 25 MeV/nucleon performed at LNS-Catania was employed in order to populate the Hoyle state of 12C and investigate the theoretically predicted molecular structures. Complete kinematic characterization of individual decay events, made possible by the CHIMERA high-granularity 4π charged particle multi-detector, reveals that 7.5±4.0% of the particle decays of the Hoyle state correspond to direct decays in three equal-energy α-particles and thus fulfill the decay criteria of an α-particle condensate. Moreover, events with increased kinetic energy dispersion in the 12C center of mass, which amount to 9.5±4.0%, point toward the occurrence of a second competing molecular configuration, a linear α-chain type. Both α-particle condensate and linear chain structures have been theoretically predicted but, to our knowledge, not experimentally confirmed so far.

Alpha-Particle Condensation in Nuclear Systems

The onset of quartetting, i.e. α-particle condensation, in symmetric and asymmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the α-particles. The critical temperature can reach values up to around 8 MeV. The disappearance of α-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 02+ of 12C is identified as an 'α-particle condensate' state. It is conjectured that such states also exist in heavier nα-nuclei, like 16O, 20Ne, etc. The sixth 0+ state in 16O is proposed as an analogue to the Hoyle state. The Gross-Pitaevski equation is employed to make an estimate of the maximum number of α particles a condensate state can contain. Possible quartet condensation in other systems is discussed briefly.

Resonance States and Alpha Condensation in 12C and 16O

Low density states near the 3α and 4α breakup thresholds in 12C and 16O, respectively, are discussed in terms of the α-particle condensation. Calculations are performed in Orthogonality Condition Model and Tohsaki–Horiuchi–Schuck–Ropke approaches. The \({0_2^+}\) state in 12C and the \({0_6^+}\) state in 16O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

Direct evidence of α-particle condensation for the Hoyle state

The fragmentation of quasi-projectiles from the nuclear reaction 40 Ca+ 12 C at 25 MeV/nucleon was used to produce excited states candidates to α-particle condensation. Complete kinematic characterization of individual decay events, made possible by the CHIMERA highgranularity 4π charged particle multi-detector, reveals that 7.5±4.0 % of the Hoyle state particle decays correspond to direct decays in three equal-energy α-particles. Moreover, events with increased kinetic energy dispersion in the 12 C center of mass, which amount to 9.5±4.0 %, point toward the occurrence of a second competing molecular configuration, of a linear α-chain.

Evidence for α-particle condensation in nuclei from the Hoyle state deexcitation

The fragmentation of quasi-projectiles from the nuclear reaction 40Ca + 12C at 25 MeV/nucleon was used to produce excited states candidates to α-particle condensation. Complete kinematic characterization of individual decay events, made possible by a high-granularity 4π charged particle multi-detector, reveals that 7.5±4.0% of the particle decays of the Hoyle state correspond to direct decays in three equal-energy α-particles.

Signatures of α-particle condensation in N = Z nuclei

At the thresholds for multi-α particle decay a phase transition of second order appears in N = Z nuclei, because the chemical potentials for nucleons in nuclear matter and in α-particles become equal. The Bose gas created by the α's strongly interacting via 0+ states in 8Be and 12C* has coherent properties because of the fact that the de-Broglie wavelength is larger than the nuclear radius. Experimental observabels are discussed, which show these coherent properties, like large radial extensions and the coherent emission of several α's.

Alpha clustering and condensation in nuclei

Low density states near the 3α and 4α breakup thresholds in 12C and 16O, respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Ropke) approaches. The 0+2 state in 12C and the 0+6 state in 16O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

ALPHA-PARTICLE CONDENSATION IN 16O

The existence of a rotational band with the [Formula: see text] cluster structure is demonstrated near the four-α threshold of 16 O in agreement with experiment. A drastic reduction of the moment of the inertia of the 0+ state at 15.1 MeV suggests that it is superfluid with four α-particle condensation. The rotational excitation of the condensate in 16 O is discussed.

ALPHA CLUSTERING AND CONDENSATION IN NUCLEI

Low density states near the 3α and 4α breakup threshold in 12 C and 16 O , respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Röpke) approaches. The [Formula: see text] state in 12 C and the [Formula: see text] state in 16 O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

CRITICAL TEMPERATURE FOR α-CONDENSATION IN ASYMMETRIC NUCLEAR MATTER: THE ASTROPHYSICAL CONTEXT

The critical temperature for α-particle condensation in nuclear matter with Fermi surface imbalance between protons and neutrons is determined. The in-medium four-body Schrödinger equation, generalizing the Thouless criterion of the BCS transition, is applied using a Hartree-Fock wave function for the quartet projected onto zero total momentum in matter with different chemical potentials for protons and neutrons.

PRODUCTION OF α-PARTICLE CONDENSATE STATES IN HEAVY-ION COLLISIONS

The fragmentation of quasi-projectiles from the nuclear reaction 40Ca+12C at 25 MeV/nucleon was used to produce excited states candidates to α-particle condensation. The experiment was performed at LNS-Catania using the CHIMERA multidetector. Accepting the emission simultaneity and equality among the α-particle kinetic energies as experimental criteria for deciding in favor of the condensate nature of an excited state, we analyze the [Formula: see text] and [Formula: see text] states of 12 C and the [Formula: see text] state of 16 O . A sub-class of events corresponding to the direct 3-α decay of the Hoyle state is isolated.

α-particle condensate states in 16O

The existence of a rotational band with the α+C12(02+) cluster structure, in which three α particles in 12C(02+) are locally condensed, is demonstrated near the four-α threshold of 16O in agreement with experiment. This is achieved by studying structure and scattering for the α+C12(02+) 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 16O suggests that it could be a candidate for the superfluid state in α-particle condensation.

PRESENT STATUS OF ALPHA-PARTICLE CONDENSATE STATES IN SELF-CONJUGATE 4n NUCLEI

Low density states near the 3α and 4α breakup threshold in 12 C and 16 O , respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Röpke) approaches. The [Formula: see text] state in 12 C and the [Formula: see text] state in 16 C are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The [Formula: see text] state in 16 C has a large component of [Formula: see text] configuration, which is another reliable evidence of the state to be of 4α condensate nature. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

FORMULATION OF ALPHA-PARTICLE CONDENSATION IN THE MACROSCOPIC LIMIT

Following closely BCS theory for pairs, an eventually viable theory for α-particle condensation (quartetting) is sketched. In the final formula the quartet wave function is replaced by a Slater determinant projected on good total momentum. The only variational field is then the single particle 0S wave function. This should reduce the numerical complexity to solve the quartet equations considerably.

ALPHA-CLUSTERS IN N=Z NUCLEI AND COHERENT EMISSION OF 2α- and 3α-CLUSTERS FROM EXCITED COMPOUND NUCLEI

Conditions for a phase change with the formation of an α-particle condensate in excited N = Z nuclei, a dilute Bose-Gas, are discussed for excitation energies around EBα = 0, These are second order phase transitions in a mixed gas of Fermions and Bosons. The de-Broglie wavelength of relative motion for α-particles in these states is much larger then the nuclear radii. The experimental observation of the decay of such condensed α-particle states is proposed, with the coherent emission of several correlated α-particles, a decay not described by the Hauser-Feshbach approach for statistical compound nucleus decay. Examples of such observations with the enhanced emission of unbound resonances of 8 Be and [Formula: see text] — clusters are discussed. The experiments involved the ISIS-GASP-detection systems at the Laboratorii Nationale di Legnaro.

Density-induced suppression of the α-particle condensate in nuclear matter and the structure of α-cluster states in nuclei

At low densities, with decreasing temperatures, in symmetric nuclear matter \ensuremath{\alpha} particles are formed, which eventually give raise to a quantum condensate with four-nucleon \ensuremath{\alpha}-like correlations (quartetting). Starting with a model of \ensuremath{\alpha} matter, where undistorted \ensuremath{\alpha} particles interact via an effective interaction such as the Ali-Bodmer potential, the suppression of the condensate fraction at zero temperature with increasing density is considered. Using a Jastrow-Feenberg approach, it is found that the condensate fraction vanishes near saturation density. Additionally, the modification of the internal state of the \ensuremath{\alpha} particle due to medium effects will further reduce the condensate. In finite systems, an enhancement of the $S$-state wave function of the center-of-mass orbital of \ensuremath{\alpha}-particle motion is considered as the correspondence to the condensate. Wave functions have been constructed for self-conjugate $4n$ nuclei that describe the condensate state but are fully antisymmetrized on the nucleonic level. These condensate-like cluster wave functions have been successfully applied to describe properties of low-density states near the $n\ensuremath{\alpha}$ threshold. Comparison with orthogonality condition model calculations in $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ shows strong enhancement of the occupation of the $S$-state center-of-mass orbital of the \ensuremath{\alpha} particles. This enhancement is decreasing if the baryon density increases, similar to the density-induced suppression of the condensate fraction in \ensuremath{\alpha} matter. The ground states of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ show no enhancement at all, thus a quartetting condensate cannot be formed at saturation densities.

Alpha Particle Condensation in Nuclear Systems

Quantum condensation of particles is one of the most amazing phenomena exhibited by many-body systems. Familiar yet striking examples known for many decades include superconductivity of metals at low temperatures and superfluidity of liquid 4He. More recently the realization of Bose-Einstein condensation of ultracold atoms in traps has created an exciting new field of quantum many-body physics. Also, atomic nuclei and neutron stars can experience quantum condensation of fermion pairs and display superfluid properties. However, in nuclear physics the most tightly bound light cluster is not a pair but a quartet, namely the alpha particle. Can we then expect α-particle condensation in nuclei? Before pursuing to this question, let us make some general remarks. It is a fact that quartetting is more pronounced in nuclei than in most other Fermi systems. And the dominance of quartetting can be traced to the fact that nucleons can exist in four different internal states: proton and neutron, each with spin up or down, all attracting each other. Therefore, a shell model picture in which the α-particle is the first doubly magic nucleus, with a filled 0S–level, is valid (see below, Fig. 2). Moreover, the α-particle is especially stiff, with its first excited state lying quite high, at ∼ 20 MeV. The search is now on for quartets in systems other than nuclei.