This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Anderson, W.D.

Bland, L.C.

Carman, D.S.

Huber, G.M.

Markham, B.C.

Miller, D.W.

Murphy, K.

Raue, B.A.

Schwandt, P.

Templon, J.A.

English

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1 KNOCKOUT REACTIONS 
STUDY OF DIPOLE RESONANCE STRENGTH IN 12C 
VIA THE REACTIONS 12C(p', p'c) 
W.D. Anderson, L.C. Bland, D.S. Carman, G.M. Huber, B.C. Markham, 
D.W. Miller, K. Murphy, B.A. Raue, P.Schwandt, J.A. Templon 
Indiana University Cyclotron Facility, Bloomington, Indiana 4 74 08 
IUCF experiment E321 is an angular correlation study of the 12~(p,p'c) reaction at 
Tp=155.8 MeV (where "en represents any charged particle). The motivation for this ex- 
periment is to gain an improved understanding of the low-excitation (E, 540 MeV) 12c 
continuum excited by small momentum transfer (qs 1.20 fm- ' ) proton inelastic scattering. 
It is anticipated that in this (q,w) domain, different spin/isopsin components of the AL=l 
particle-hole response will predominate. The angular correlation function of coincident 
charged-particle decays is expected to help identify the multipolarity of overlapping reso- 
nances in the intermediate state as well as distinguish resonance excitation from the non- 
I resonant quasifree knockout "background" which plagues inclusive measurements.' The 
experiment was performed at three different proton scattering angles to aid the multipole 
decomposition. Data for the inclusive cross section and analyzing power for the ' 2~ (p ,p ' )  
reaction were obtained simultaneously with the exclusive l2 C (p ,p'c) data. Measurements 
were completed at three angles: OPt=14.3, 19.0, and 24.0". 
The K600 spectrometer was utilized to detect inelastically scattered protons. The 
1 forward-angle limit for the spectrometer of 14.3O was imposed by the exit pipe necessary 
for transporting the beam to the external faraday cup. Coincident charged particles were 
detected in a coplanar geometry by an array of eight counter telescopes mounted in the 
61 cm vacuum chamber. Four telescopes were placed on the left and right sides of the beam 
in 25" intervals covering the angular range from 0" to 180° for charged particle decays 
from 12c* resonant states. Each telescope consisted of a 2.54 cm diameter, 0.01 cm thick 
(AE) silicon surface barrier detector and a 2.54 cm diameter, 0.5 cm thick (E) lithium- 
drifted silicon detector. The detectors were operated at O0 C to optimize their pulse-height 
resolution and to minimize radiation damage. Each detector pair was mounted in a 0.64 cm 
thick brass shielding enclosure that had a circular aperture viewing the target. The solid 
angle for all but the most forward telescope was 5 msr. Singles rates in the telescopes were 
less than 10 kHz for a luminosity of 56.8 x lo3' ~ m - ~ s - ' .  Particle identification was 
accomplished using either AE vs. E or time of flight vs. E correlations. Clean separation 
of all particle groups was achieved covering the dynamic range from the 1-MeV telescope 
detection threshold up to 25-MeV protons. 
Event triggering was accomplished by forming the logical OR of the AE and E detec- 
tors of each telescope. The eightfold OR of the telescope triggers independently latched 
I pulse-height and timing data for the detector array. The standard focal plane trigger 
(scintillator coincidence) was used to latch data from the vertical drift chambers and the 
scintillators. A sample of the singles data from the K600 focal plane and the detector array 
was read out by the computer for the inclusive (p,p') measurements and for monitoring 
purposes. A coincidence between any member of the detector array and the K600 focal 
plane triggered computer readout of all data. The resolving time of the overlap was long 
enough to permit direct measurements of accidental coincidences necessary for the ofline 
analysis. CAMAC data was cleared by a hardware signal for noncoincident events. 
An analysis of the (p,p'c) data has been completed including most of the essential 
corrections to the data. These corrections include calculating detection efficiencies of par- 
ticle "c" accounting for detector thresholds, energy-loss effects through the thick target, 
and finite-geometry effects including kinematic variations, subtraction of accidental coin- 
cidences, correct ion for vertical drift chamber efficiency, and dead-time corrections. The 
energy correlation for the l2 c (p,2p) reaction for the angle pair BKeoo=14.30 and 9,= -64.3O 
is shown in Fig. 1. The diagonal loci represent states of "B-the residual nucleus. The 
po+ll~(g.s . )  channel is observed to be the most strongly populated. Summed energy 
resolution of 1300 keV was obtained for the (p,2p) reaction in this experiment. The reso- 
lution obtained for the (p,pta) data was significantly worse due to energy-loss effects in the 
thick (2 mg/cm2) target. The ratio of real to accidental coincidences was greater than 8% 
Events within a given locus are projected onto the horizontal axis yielding that fraction 
of the proton inelastic scattering yield coincident with the particular charged particle "c". 
In the following we present results for or and po coincidences. 
opt = 14.3 deg, Ope = -64.3 deg 
I - - . -  -,--.- - - r  --- --- r- - - ----- -T-- - -- I- - - -- 
1500 2500 3500 4500 5500 6500 7500 8500 8500 
+-- Scattered Proton Momentum (arb. units) 
Figure 1. Energy correlations for 12~(p ,2p)  at Tp=155.8 MeV, 6,1=14.3", 8,=-64.3". 
Figure 2. Comparison of the inclusive, po-gated, and a-gated 12C(p,p1) spectra at 
Op=14.30 (lab). Coincident particles are detected at 8,=-64.3O (lab). 
Fig. 2 compares the 14.3O inclusive spectrum to the exclusive spectra for coincident 
po and a particles detected at -64.3O. This correlation angle is essentially parallel to the 
momentum transfer direction and thus is at nearly O0 in the 12c* rest frame. Below 18 
MeV the inclusive spectrum is dominated by the excitation of the broad 2+,T=0 resonance 
at 15.4 MeV and the narrow 1 + , ~ = l  (15.1 MeV) and 2 + , ~ = 1  (16.1 MeV) states. The 
threshold for proton emission from 12C is at E,=15.96 MeV. Proton decays from the 16.1 
MeV state are not observed due to our detection threshold and use of a thick target. 
The broad 15.4 MeV resonance is prominent in the (p,pla) spectrum. The yield from 
this state is found to be strongly peaked around the momentum transfer direction. At 
larger correlation angles, significant yields are observed from the 16.1 MeV state. This is 
consistent with the known large partial width for decay of this state into * B e ( 2 + ) + ~ ~ . ~  
There is only weak evidence for a1 decay from the 15.1 MeV state, which is again consistent 
with its known small partial width.2 
Peaks from the 18.35 MeV (2- ,T=O) and 19.40 MeV (2- ,T=l) states are also promi- 
nent in the inclusive yield at small q. The former is observed to have both po and a decays. 
A detailed examination of the a energy distribution indicates that there is no evidence for 
a0 decays; only a1 decays are necessary to understand the spectrum. This is consistent 
with the 2- spin assignment (aO decays are forbidden by parity conservation). The similar- 
ity of the width and centroid of the 18.35 MeV peak for the a-gated and po-gated spectra 
suggest observation of only a single state even though there is published evidence of more 
than one state near 18.4 MeV.2 We find no evidence of yield from the 19.40 MeV state 
in any of our (p,pta) spectra which is consistent with the T = l  assignment for this state. 
The po yields have been extracted by peakfitting the exclusive spectrum. No background 
is necessary to include in the analysis if Lorentzian functions are used for the lineshapes. 
Fig. 3 displays the 2- data compared with angular correlation calculations. The cal- 
culations were performed assuming sequential resonance excitation and decay. The exci- 
- 
18.35 MeV (2-;O) 
- - 
1 19.4 MeV (2-;I) 
- 
I I I I I I I I I I I I I I , ~  
Figure 9. Double-differential cross section and analyzing-power correlations for po decays 
from the 2- states at 18.35 and 19.40 MeV. The cross section is plotted against the decay 
proton polar angle in the 12C* rest frame (with the &axis along the (p,pf) momentum 
transfer direction.) Positive angle denotes rotation towards beam left in the scattering 
plane. The curves are results of DWIA correlation calculations discussed in the text. 
The different curves represent calculations using the different components of the N-N 
interaction: solid curve - full interaction; dotted curve - central-spin only; dashed curve - 
spin-orbit only; and dot-dashed curve - tensor only. 
tation was calculated using a standard DWIA code and the Love-Franey nucleon-nucleon 
intera~tion.~ The scattering amplitudes from this calculation were used to compute the 
density matrix for the l2 C * m-states (nuclear spin projections.) The angular correlation 
function is calculated given this m-state density matrix and assumptions about the orbital 
angular momentum involved in the decay. The transition density for both states is assumed 
to be the single particle/hole configuration, ld5,21P~,?2, coupled to JX=2-. A previous 
study of proton inelastic scattering cross section and spin observable angular distributions 
identified this as the dominant configuration for these  state^.^ For the angular correlation 
calculations, we assumed that the po decay is pure d wave from the unbound Id5/, orbital. 
The branching ratio to the p o + l l ~  channel was assumed to be 100%. There is good agree- 
ment between this calculation and the pattern observed for the 18.35 MeV transition when 
the calculated correlation function is scaled by 0.6. Inclusion of po decay from the unbound 
2s1j2 orbital would tend to make the correlation function more isotropic (enhancing the 
agreement.) For the 19.40 MeV state, the data displays a forelaft asymmetry which the 
calculation does not reproduce. Furthermore, the data appear more strongly peaked along 
the momentum transfer direction than does the calculation. 
Fig. 3 also shows the sensitivity of the calculated angular correlation function to var- 
ious parts of the NN interaction used to drive the transition. The T=O state is observed 
to result from a constructive interference of amplitudes involving the spin-orbit and ten- 
sor interactions. The T= 1 state is dominated by the central spin-dependent interaction 
destructively interfering with small tensor and spin-orbit contributions. The resulting cor- 
relation patterns show largest differences in angular ranges which are not easily measured 
experimentally. Significant differences are observed for the correlation spin-asymmetry 
function (measured as the incident spin upldown asymmetry as a function of the corre- 
lation angle). The simple model described above does not reproduce the features of the 
correlation spin asymmetry, suggesting that this observable may be sensitive to physics not 
yet included in the calculation ( e. g. more complicated transition densities or contributions 
from other partial waves in the decay.) 
Near E,=22 MeV, the inclusive (p,pf) spectrum shows a broad bump atop a featureless 
background. The enhancment has been determined from previous inclusive studies1 to be 
the giant dipole resonance (GDR) observed in photoabsorption s t ~ d i e s . ~  In the (p,pfpo) 
exclusive spectrum, the background observed in the inclusive scattering is greatly reduced, 
but the peak-to-background ratio is not as improved for the GDR as it was in the case of 
the 2- states. The shape of the po-gated spectrum in this region of excitation is observed 
to change as a function of the correlation angle. This behavior may be consistent with 
correlation-angle dependence of contributions from other 12c* resonances of different J". 
Sizeable forelaft asymmetries are observed in the correlation functions for all energy bins. 
These asymmetries are likely due to coherent contributions from the pp quasifree knockout 
"background" which are peaked at correlation angles near q - i .e.  forward angles in the 
12c* rest frame. 
Yields have been extracted by summing the triple-differential cross section in energy 
bins of 0.5 MeV (Fig. 4). No attempt has been made to subtract an (arbitrary) background. 
Thus, contributions from quasifree pp scattering are included with those from sequential 
resonance excitation and decay. Near E,=22 MeV, the angular correlation patterns vary 
Ex = 22.5 MeV 
0,. = 14.3" 
10 
- - 
Ex = 29.5 MeV : 
Opt = 14.3" 
- 
Figure 4. Double-differential cross section correlations for 0.5 MeV wide continuum slices 
centered at E,=22.25 and 29.25 MeV. The curves are results of the 3D calculations dis- 
cussed in the text. 
significantly with energy bin and the q dependence of these patterns is large. This behavior 
is different from the higher excitation energy data (Ex 2 2 5  MeV) where the correlation 
function behavior is similar in all excitation energy bins and the q dependence is weak. 
This provides evidence that the angular correlation data will permit identification of the 
AL=l yield excited by (p,pl) in the region of the GDR. The higher-excitation data are 
probably consistent with non-resonant quasifree pp scattering. 
A large peak is observed in the (p,pla) spectrum in the vicinity of the GDR. The an- 
gular correlation and q-dependence of the yield from this peak are similar to that observed 
for the Ex=18.35 MeV state. This is suggestive of dominance of AL=l for the population 
of the state. The sizeable a! decay yield suggests the occurrence of a T=O intermediate 
state. A J"=l-,T=O state, nearly degenerate with the GDR in 12c, may explain sizeable 
differences in the (r,po) and (r,no) cross sections reported in this region of exci ta t i~n .~  
In Fig. 4 we compare our data at higher excitation energies to distorted-wave calcula- 
tions using the program 3 ~ . ~  In these calculations, the transition density used in the "tp" 
prescription for the interaction potential is replaced by the product of the bound-state 
wave function of the struck nucleon and a wave function describing the relative motion of 
the unbound system p o + l l ~ .  The latter is the solution to the Schrodinger equation using 
a complex potential. In general, this potential will have resonant solutions for specific 
partial waves at certain values of the relative energy. It is these single-particle resonances 
which are involved in constructing the "giant" resonances observed in the inclusive spec- 
trum. In the calculations presented, the p o + l l ~  potential has a resonance in the d5/2 
partial wave at the excitation energy of the GDR. The potential also includes non-zero 
phase shifts for the other (non-resonant) partial waves. Inclusion of contributions from 
both resonant and non-resonant partial waves represents the coherent addition of quasifree 
knockout amplitudes with the amplitude which describes the GDR excitation and decay. 
In the present model, the latter does not describe decay from a 12C* intermediate state of 
good J" and T, rather it is simply a single-particle resonance. The shape of the angular 
correlation pattern near the resonance and at higher excitation energy is fairly well de- 
scribed by this calculation. The q dependence of the data is also reasonably well described. 
The calculations all have the same normalization factor (m 0.7). The agreement is better 
for the higher excitation energies and for the more forward (in the 12c* rest frame) decay 
proton angles, where the intermediate (12C) state structure effects should be diminished 
relative to the nonresonant scattering. It is anticipated that an improved description of 
the exclusive yields can be obtained by using a transition density from the continuum shell 
model. 
1. M. Buenerd, P. Martin, P. de Saintignon and J. M. Loiseaux, Nucl. Phys. A288, 377 
(1977). 
2. F. Ajzenberg-Selove, Nucl. Phys. A433, 1 (1985). 
3. Computer Codes ALLWRLD and TAMURA, F. Petrovich e t  al., unpublished; 
M. A. Franey and W. G. Love, Phys. Rev. C 31, 488 (1985). 
4. K. W. Jones, e t  al., Phys. Lett. 128B, 281 (1983). 
5. M. T. Collins, e t  al., Phys. Rev. C 26, 332 (1982). 
6. N. S. Chant and P. G. Roos, Phys. Rev. C 15, 57 (1977). N. S. Chant and P. G. 
Roos, Phys. Rev. C 27, 1060 (1983). 


Study of Dipole Resonance Strength in 12-C via the Reactions 12-C(pol.p,p'c)

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Study of Dipole Resonance Strength in 12-C via the Reactions 12-C(pol.p,p'c)

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