86
W. H. Dickhoff
3 40 Ca(e, e p) 39 K Reaction and Spectroscopic Factors
Several papers have appeared in the past questioning the relevance of spectroscopic
factors [22, 23] and the possibility of measuring momentum distributions or
occupation numbers [24]. It is useful to point out that Fermi liquid theory developed
by Landau [25–27] relies on the notion of a quasiparticle with a corresponding
strength (spectroscopic factor) near the Fermi surface that can be experimentally
probed through specific heat measurements [28]. For finite systems like atoms
and molecules the corresponding information is accessed by analyzing the (e, 2e)
reaction [2, 29, 30]. Similar efforts in nuclear physics have attempted to extract
spectroscopic factors from the (e, e p) reaction [31] for valence hole states in mostly
double-closed-shell nuclei (see also Refs. [2, 32]).
Experimental results of the (e, e p) reaction have been included in the local
DOM in the past by employing the extracted spectroscopic factors [33, 34] in fits
with local potentials to the 40 Ca and 48 Ca nuclei [35, 36] and to data in other
domains of the chart of nuclides [15]. A better approach has now been implemented
based on the non-local DOM developments [3, 37, 38] that also allows an assessment
of the quality of the distorted-wave impulse approximation (DWIA) that is utilized
to describe the reaction. We note that the conventional analysis of the reaction
employed standard local non-dispersive optical potentials to describe the proton
distorted waves [39]. We have thus arrived at a stage with the DOM that all
ingredients for the DWIA description can be supplied from one self-energy that
generates the proton distorted waves at the desired outgoing energies, as well as the
overlap function with its normalization. Important to note is that these ingredients
are not adjusted in any way to (e, e p) data.
The non-local DOM description of 40 Ca data was presented in [37]. In the mean
time, additional experimental higher-energy proton reaction cross sections [40]
have been incorporated which caused some adjustments of the DOM parameters
compared to [37]. Adjusting the parameters from the previous values [37] to
describe these additional experimental results leads to an equivalent description for
all data except these reaction cross sections. The required additional absorption at
higher energies leads to a loss of strength below the Fermi energy, reducing the
spectroscopic factors by about 0.05 compared to the results reported in [37], thereby
also documenting the importance of reaction cross section data for protons at higher
energy.
Using a recent version of the code DWEEPY [41], our DOM ingredients have
been utilized to describe the knockout of a proton from the 0d
3
2 and 1s
1
2 orbitals
in 40 Ca with fixed normalizations of 0.71 and 0.60, respectively [42]. The DOM
at present generates only one main peak for 1s
1
2 orbit so the employed value of
0.60 for the spectroscopic factor takes into account the experimentally observed
low-energy fragmentation. Experimental data were obtained at Nikhef in parallel
kinematics for three outgoing proton energies: 100, 70, and 135 MeV. Data for
the latter two energies were never published before. The resulting description of
the (e, e p) cross sections is at least as good as the Nikhef analysis which yielded
W. H. Dickhoff
3 40 Ca(e, e p) 39 K Reaction and Spectroscopic Factors
Several papers have appeared in the past questioning the relevance of spectroscopic
factors [22, 23] and the possibility of measuring momentum distributions or
occupation numbers [24]. It is useful to point out that Fermi liquid theory developed
by Landau [25–27] relies on the notion of a quasiparticle with a corresponding
strength (spectroscopic factor) near the Fermi surface that can be experimentally
probed through specific heat measurements [28]. For finite systems like atoms
and molecules the corresponding information is accessed by analyzing the (e, 2e)
reaction [2, 29, 30]. Similar efforts in nuclear physics have attempted to extract
spectroscopic factors from the (e, e p) reaction [31] for valence hole states in mostly
double-closed-shell nuclei (see also Refs. [2, 32]).
Experimental results of the (e, e p) reaction have been included in the local
DOM in the past by employing the extracted spectroscopic factors [33, 34] in fits
with local potentials to the 40 Ca and 48 Ca nuclei [35, 36] and to data in other
domains of the chart of nuclides [15]. A better approach has now been implemented
based on the non-local DOM developments [3, 37, 38] that also allows an assessment
of the quality of the distorted-wave impulse approximation (DWIA) that is utilized
to describe the reaction. We note that the conventional analysis of the reaction
employed standard local non-dispersive optical potentials to describe the proton
distorted waves [39]. We have thus arrived at a stage with the DOM that all
ingredients for the DWIA description can be supplied from one self-energy that
generates the proton distorted waves at the desired outgoing energies, as well as the
overlap function with its normalization. Important to note is that these ingredients
are not adjusted in any way to (e, e p) data.
The non-local DOM description of 40 Ca data was presented in [37]. In the mean
time, additional experimental higher-energy proton reaction cross sections [40]
have been incorporated which caused some adjustments of the DOM parameters
compared to [37]. Adjusting the parameters from the previous values [37] to
describe these additional experimental results leads to an equivalent description for
all data except these reaction cross sections. The required additional absorption at
higher energies leads to a loss of strength below the Fermi energy, reducing the
spectroscopic factors by about 0.05 compared to the results reported in [37], thereby
also documenting the importance of reaction cross section data for protons at higher
energy.
Using a recent version of the code DWEEPY [41], our DOM ingredients have
been utilized to describe the knockout of a proton from the 0d
3
2 and 1s
1
2 orbitals
in 40 Ca with fixed normalizations of 0.71 and 0.60, respectively [42]. The DOM
at present generates only one main peak for 1s
1
2 orbit so the employed value of
0.60 for the spectroscopic factor takes into account the experimentally observed
low-energy fragmentation. Experimental data were obtained at Nikhef in parallel
kinematics for three outgoing proton energies: 100, 70, and 135 MeV. Data for
the latter two energies were never published before. The resulting description of
the (e, e p) cross sections is at least as good as the Nikhef analysis which yielded