4.3 The Particle-Rotor Model in the Berggren Basis
173
4.3.4 Weakly Bound and Unbound Atomic Nuclei
Studies of exotic nuclei far from the valley of beta-stability reveal novel features,
such as the formation of nuclear halo [64, 98], near-threshold clustering [99–102],
and the presence of new types of correlations [103]. In all these cases, atomic
nucleus exhibits properties which are characteristic of the open quantum system
whose properties depend on the coupling to reaction channels [104]. While the
impact of reaction channels on nuclear structure has been recognized [49], the
fact that some highly excited configurations can be interpreted in terms of nuclear
clusters or nuclear molecules that experience collective motions such as rotations
and vibrations is quite astonishing.
The success of the collective model of atomic molecules is based on the validity
of the Born-Oppenheimer approximation [105] that relies on the huge difference of
time scales for single-electron and ionic motions. The time-scale separation between
single-nucleon and collective nuclear motion in atomic nuclei is small and, hence,
the adiabatic approximation is expected to be badly violated [106]. One may ask,
therefore, why a highly excited state, undergoing rapid particle emission, can be
looked at using simple notions such as rotating or vibrating fields, or potentials,
common for all nucleons. A good example is the spectrum of 12 C which was
discussed in the geometric/algebraic language of three α-particle arrangements
[107].
A related issue concerns the interpretation in terms of a nucleus, or a nuclear state
of the broad resonances observed in scattering experiments. An excellent example
is provided by the 0
+
1 , 2
+
1 , 4
+
1 resonances of 8 Be which have the width 5.57 eV,
1.15 MeV, and about 3.5 MeV, respectively [108]. Let us consider the single-particle
time scale. The average time it takes for a nucleon to go across a light nucleus
(A ≈ 10) and come back can be roughly estimated at T s.p. ≈ 1.3·10 −22 s [109], and
corresponds to the time scale needed to form the nuclear mean field. Consequently,
one is tempted to conclude that broad scattering features with T 1/2 < T s.p. (or Γ >
3.5 MeV for A ≈ 10) can hardly be interpreted as the nuclear states [110].
Obviously, there is no sharp borderline that separates genuine nuclear states from
broad structures seen in scattering experiments, and this often results in interpretational difficulties [111]. Moreover, a quantitative experimental characterization
of broad resonances embedded in a large nonresonant background is not always
possible. For instance, the extraction of experimental widths is usually modeldependent and relies on approximations [112, 113].
In order to study nuclear systems, one uses a particle-plus-core coupled-channel
approach, based on the Berggren ensemble, which has been applied in Sects. 4.3.2
and 4.3.3 for the case of dipolar and quadrupolar anions. It has been shown in the
dipolar case that below the ionization threshold, the motion of the valence electron
is strongly coupled to the collective rotation of the molecule, forming rotational
states. Above the ionization threshold, however, a rapid decoupling of the electron’s
motion from the rotational motion of the molecule takes place, thus leading to a
disappearance of a collective rotational band. This observation brings the question
173
4.3.4 Weakly Bound and Unbound Atomic Nuclei
Studies of exotic nuclei far from the valley of beta-stability reveal novel features,
such as the formation of nuclear halo [64, 98], near-threshold clustering [99–102],
and the presence of new types of correlations [103]. In all these cases, atomic
nucleus exhibits properties which are characteristic of the open quantum system
whose properties depend on the coupling to reaction channels [104]. While the
impact of reaction channels on nuclear structure has been recognized [49], the
fact that some highly excited configurations can be interpreted in terms of nuclear
clusters or nuclear molecules that experience collective motions such as rotations
and vibrations is quite astonishing.
The success of the collective model of atomic molecules is based on the validity
of the Born-Oppenheimer approximation [105] that relies on the huge difference of
time scales for single-electron and ionic motions. The time-scale separation between
single-nucleon and collective nuclear motion in atomic nuclei is small and, hence,
the adiabatic approximation is expected to be badly violated [106]. One may ask,
therefore, why a highly excited state, undergoing rapid particle emission, can be
looked at using simple notions such as rotating or vibrating fields, or potentials,
common for all nucleons. A good example is the spectrum of 12 C which was
discussed in the geometric/algebraic language of three α-particle arrangements
[107].
A related issue concerns the interpretation in terms of a nucleus, or a nuclear state
of the broad resonances observed in scattering experiments. An excellent example
is provided by the 0
+
1 , 2
+
1 , 4
+
1 resonances of 8 Be which have the width 5.57 eV,
1.15 MeV, and about 3.5 MeV, respectively [108]. Let us consider the single-particle
time scale. The average time it takes for a nucleon to go across a light nucleus
(A ≈ 10) and come back can be roughly estimated at T s.p. ≈ 1.3·10 −22 s [109], and
corresponds to the time scale needed to form the nuclear mean field. Consequently,
one is tempted to conclude that broad scattering features with T 1/2 < T s.p. (or Γ >
3.5 MeV for A ≈ 10) can hardly be interpreted as the nuclear states [110].
Obviously, there is no sharp borderline that separates genuine nuclear states from
broad structures seen in scattering experiments, and this often results in interpretational difficulties [111]. Moreover, a quantitative experimental characterization
of broad resonances embedded in a large nonresonant background is not always
possible. For instance, the extraction of experimental widths is usually modeldependent and relies on approximations [112, 113].
In order to study nuclear systems, one uses a particle-plus-core coupled-channel
approach, based on the Berggren ensemble, which has been applied in Sects. 4.3.2
and 4.3.3 for the case of dipolar and quadrupolar anions. It has been shown in the
dipolar case that below the ionization threshold, the motion of the valence electron
is strongly coupled to the collective rotation of the molecule, forming rotational
states. Above the ionization threshold, however, a rapid decoupling of the electron’s
motion from the rotational motion of the molecule takes place, thus leading to a
disappearance of a collective rotational band. This observation brings the question