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Inelastic electron scattering in 32S
Volume
24B, number
8
PHYSICS
INELASTIC
LETTERS
17 April
SCATTERING
ELECTRON
L. L. HILL U.S. Naval Ordnance Laboratory, Silver Spring,
1967
IN 32s
Maryland
and H. ~~BERALL* The Catholic
University Received
of America, 1 February
Washington,
D. C.
1967
The El and M2 matrix elements for inelastic electron scattering and photoexcitation of the giant resonance states in 32s are presented. A sequence of dominant levels similar to those in 12C is found but at generally lower energies. In particular, the 2- spinflip state which should rise up for large momentum transfers, lies here at 13.5 MeV.
The Brown model [1,2] has led to considerable success in accounting for many of the properties of the giant dipole resonance observed in the 15 to 25 MeV region of a number of nuclei. In particular, the magic or double magic nuclei 12C, 160 and 40Ca have received rather exhaustive treatment [ 2-6 , and some work has been done [7-91 on 28Si and A S. In the framework of the Brown model, one assumes that the resonance states are composed of a linear combination of particlehole states where the residual interaction provides the mixing. The unperturbed energies are taken as the sum of the single particle and single hole energies from experimental data of adjacent nuclei. In this note, the Brown model was applied to 328 using a Serber residual interaction. The results were then used to calculate the El and M2 matrix elements for 180 degree inelastic electron scattering. Experimental data for 338 are quite good [lo] and gives the location of the If +, 2p+ and 2~; particle states at 2.94, 3.22 and 5.71 MeV. The Id; particle is the ground state of 338. The spin and parity assignments to the 31s spectrum are not known. Comparing the 318 and 3lP spectrum [lo], and further comparing with shell model calculations [ll], it is concluded that the 2.28 MeV level in 3% is 3’ and therefore the Id+ hole state. The lp$ hole was determined by Bolen and Eisenberg [‘I] to be 5.1 MeV below the Id; hole. The location of the lp+ hole is then obtained by assuming that the I * s splitting is the same as that of 160 (i.e. 6.15 MeV). The location of the If; level is taken 364
to be 2.4 MeV above the 2pi level based on the 41Ca data [5,6]. Finally, the 2s.~ hole is the ground state of 313. The resultant unperturbed particle-hole energies (Eo) for 328 are given in the third row of table 1. The residual interaction was taken as a Serber force with parameters adjusted to fit low-energy n-p scattering data [3]. The unperturbed states are described using a harmonic oscillator wave function. The harmonic oscillator range was taken as 1.9fm which is an average of the values obtained from high and low energy experiments [12]. The resultant eigenvalues (E) and eigenvectors are given in table 1. The El and M2 squared, reduced matrix elements needed for inelastic electron scattering [13] at 180 degrees were then calculated and are presented in figs. land 2 as a function of momentum transfer. Since the matrix elements for photoexcitation are the same as the 180 degree electron scattering elements at a momentum transfer corresponding to the eigen energies, they were determined and their percentage contributions are listed in table 1. It is seen that the I-, 17.4 MeV level accounts for 65 percent of the photoabsorption strength (Quadrupole photoabsorption is negligible), whereas the l-, 24 MeV level and the 2-, 13.5 MeV level are dominant in inelastic electron scattering above about 50 MeV. The situation is similar to that [3] in 12C and l60 * Supportedby a grant of the National Science Foundation.
Volume
24B,
Energy
number
levels,
8
PHYSICS
wave
LETTERS
17 April
Table 1 percentage dipole (DS) and quadrupole (QS) strengths T = 1, lliw particle-hole states in 32s.
functions,
for
the JT = l-
Hole
2s;
Id+
Id;
2s;
lP+
Id;
2s;
IdI
lP$
part
2P_‘2
2P$
lf;
2P;
Id;
2P;
lf+
If+
Id{
9.6
11.6
11.9
12.1
13.9
14.4
14.5
16.8
20.1
EO
E 11.2 13.4 14.0 14.8
1967
and 2-,
DS(%) 0.96 -0.08 0.02 -0.16
-0.26
0.10
0.01
-0.02
-0.01
0.0
-0.07
0.62
0.76
0.20
-0.01
-0.02
0.6
-0.28
0.72
-0.61
0.01
-0.00
0.68
-0.15
0.66
-0.62
17.4
0.21
0.68
-0.03
-0.29 0.09
1D
0.16
0.03
1.9
0.19
0.10
13.9
0.12
0.13
65.2
18.3
0.02
0.08
-0.06
0.09
-0.13
0.86
24.0
0.01
0.02
-0.02
0.11
-0.24
0.42
0.86
BSO (%)
6.6
16.1
4.0
4.2
55.1
11.4
35.6
-0.47
2.5 15.9
QS (%) 11.0
0.97
0.21
0.06
0.01
0.03
0.01
0.03
0.02
12.8
0.03
0.38
0.92
0.05
0.13
0.00
0.02
0.01
0.0
13.5
0.20
0.87
0.35
0.16
0.18
0.09
0.08
0.03
34.4
15.0
0.02
0.03
0.03
0.65
0.08
0.76
0.04
0.00
0.1
15.6
0.06
0.08
0.17
0.04
0.96
0.13
0.12
0.00
15.5
16.1
0.06
0.20
0.06
0.73
0.11
0.61
0.19
0.03
11.7
17.9
0.04
0.04
0.02
0.12
0.09
0.15
0.94
0.26
12.3
21.5
0.03
0.03
0 .oo
0.06
0.01
0.06
0.25
0.96
23.8
8.2
0.5
QS, (%)
8.2
37.1
2 B
but one should note that the corresponding states, especially the 2’ state, are now generally considerably lower in energy. The 17.4 and 18.3 MeV levels are in close agreement with the 17.6 and 18.2 MeV levels observed in several (y, n) and (p, 36) experiments [14-171. The 24 MeV level is in agreement with the 24 MeV level observed by Bolen and Whitehead [17] while the 14.8 MeV level may well correspond to the 15 MeV level observed by Dearnaley et al. [16]. Additional major peaks observed by these experiments exists at 19.7, 21.2, 22.8 and 25 MeV. Although the energy level agreement between experiments is good, the relative amplitude of the levels is not. The present calculation indicates that the dipole strength is concentrated at about 17.5 MeV. This is supported by some of the experiments, while others indicate that the strength is concentrated at about 20 MeV. Kossanyi-Demay and Vanpraet [18] have performed the 180 degree inelastic electron scattering ex-
13.3
0.0
17.7
2.2
15.0
periment for a single beam energy of 51 MeV, q N 80 MeV/c , About 15 peaks were observed between about 10 and 28 MeV, many of which agree well with the photoabsorption experiments mentioned above. The peak amplitude of the resonances observed in this range do not vary by more than about 30 percent. In particular, no strong peaks are observed which would indicate the influence of the 24 MeV, l- level and 13.5 MeV, 2level predicted in this calculation. It is hoped that future experiments at higher momentum transfers will be performed. Identical calculations were carried out for 28Si where the unperturbed energy spectrum was taken from Bolen and Eisenberg [7]. Results for the energy levels and wave functions are in reasonable agreement with the l- calculations of Farris and Eisenberg [9]. Seaborn and Eisenberg [ 191 have calculated the E 1 matrix elements and show that the 26 MeV level in 28Si is strongly dominant for momentum transfers above 50 MeV/c 365
Volume
24B, number 8
PHYSICS
LETTERS
17 April
1967
r
2a
4
(MEV/O
Fig.2. Squared, reduced matrix elements for inelastic electron scattering at 180’ from the JB = 2- particlehole states in 32~.
2. G. E. Brown, L. Castillejo 3. q(MEV/'Zi
4. Fig. 1, Squared, reduced matrix elements for inelastic electron scattering at 180’ from the Jr = l- particlehole states in 32~.
5. 6.
as in the present
329 results. Our calculations for 23Si verify this El behaviour and also show a very strong, again rather low-lying (14.3 MeV), M2 element in this high momentum transfer regime. authors would like to thank Mr. S. A. Farris, Prof. J.M. Eisenberg, Dr. P. Kossanyi-Demay, Dr. G. J.Vanpraet, and Prof. W. C. Barber for furnishing their results in advance of publication . The
References
1. G.E.Brown (1959) 472.
366
and M.Bolsterli,
Phys.
Rev.
Letters
3
7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
and J.A. Evans, Nucl. Phys. 22 (1961) 1. F.H.Lewis and J.D.Walecka, Phys. Rev. 133 (1964) B 849. N.Vinh-Mau and G.E.Brown, Nucl. Phys. 29 (1962) 89. V. V. Balashov, V.G.Shevchenko and N. P. Yudin, Nucl. Phys. 27 (1961) 323. L.J.Weigert and J.M.Eisenberg, Nucl. Phys. 53 (1964) 508. L.N.Bolen and J.M.Eisenberg, Phys. Rev. Letters 9 (1964) 52. B. M.Spicer, Au&. J. Phys. 18 (1965) 1. S.A.Farris and d.M.Eisenberg, private communication. P.M.Endt and C.Van der Leun, Nucl. Phys. 34 (1962) 1. P.W.M.Glaudermans et al., Nucl. Phys. 56 (1964) 548 B.C.Carlson and LTalmi, Phys. Rev. 96 (1954) 436. R.Willey, Nucl. Phys. 40 (1963) 529. M.Kimura et al., J. Phys. Sot. Japan 18 (1963) 477. F.W.K.Firk, NucL. Phys. 52 (1964) 437. G.Dearnaley et al., Nucl. Phys. 64 (1965) 177. L.N.Bolen and W.D.Whitehead, Phys. Rev. 132 (1963) 2251. P, Kossanyi-Demay and G. Vanpraet, private communication. J.B.Seaborn and J.M.Eisenberg, Nucl. Phys. 63 (1965) 496.
24B, number
8
PHYSICS
INELASTIC
LETTERS
17 April
SCATTERING
ELECTRON
L. L. HILL U.S. Naval Ordnance Laboratory, Silver Spring,
1967
IN 32s
Maryland
and H. ~~BERALL* The Catholic
University Received
of America, 1 February
Washington,
D. C.
1967
The El and M2 matrix elements for inelastic electron scattering and photoexcitation of the giant resonance states in 32s are presented. A sequence of dominant levels similar to those in 12C is found but at generally lower energies. In particular, the 2- spinflip state which should rise up for large momentum transfers, lies here at 13.5 MeV.
The Brown model [1,2] has led to considerable success in accounting for many of the properties of the giant dipole resonance observed in the 15 to 25 MeV region of a number of nuclei. In particular, the magic or double magic nuclei 12C, 160 and 40Ca have received rather exhaustive treatment [ 2-6 , and some work has been done [7-91 on 28Si and A S. In the framework of the Brown model, one assumes that the resonance states are composed of a linear combination of particlehole states where the residual interaction provides the mixing. The unperturbed energies are taken as the sum of the single particle and single hole energies from experimental data of adjacent nuclei. In this note, the Brown model was applied to 328 using a Serber residual interaction. The results were then used to calculate the El and M2 matrix elements for 180 degree inelastic electron scattering. Experimental data for 338 are quite good [lo] and gives the location of the If +, 2p+ and 2~; particle states at 2.94, 3.22 and 5.71 MeV. The Id; particle is the ground state of 338. The spin and parity assignments to the 31s spectrum are not known. Comparing the 318 and 3lP spectrum [lo], and further comparing with shell model calculations [ll], it is concluded that the 2.28 MeV level in 3% is 3’ and therefore the Id+ hole state. The lp$ hole was determined by Bolen and Eisenberg [‘I] to be 5.1 MeV below the Id; hole. The location of the lp+ hole is then obtained by assuming that the I * s splitting is the same as that of 160 (i.e. 6.15 MeV). The location of the If; level is taken 364
to be 2.4 MeV above the 2pi level based on the 41Ca data [5,6]. Finally, the 2s.~ hole is the ground state of 313. The resultant unperturbed particle-hole energies (Eo) for 328 are given in the third row of table 1. The residual interaction was taken as a Serber force with parameters adjusted to fit low-energy n-p scattering data [3]. The unperturbed states are described using a harmonic oscillator wave function. The harmonic oscillator range was taken as 1.9fm which is an average of the values obtained from high and low energy experiments [12]. The resultant eigenvalues (E) and eigenvectors are given in table 1. The El and M2 squared, reduced matrix elements needed for inelastic electron scattering [13] at 180 degrees were then calculated and are presented in figs. land 2 as a function of momentum transfer. Since the matrix elements for photoexcitation are the same as the 180 degree electron scattering elements at a momentum transfer corresponding to the eigen energies, they were determined and their percentage contributions are listed in table 1. It is seen that the I-, 17.4 MeV level accounts for 65 percent of the photoabsorption strength (Quadrupole photoabsorption is negligible), whereas the l-, 24 MeV level and the 2-, 13.5 MeV level are dominant in inelastic electron scattering above about 50 MeV. The situation is similar to that [3] in 12C and l60 * Supportedby a grant of the National Science Foundation.
Volume
24B,
Energy
number
levels,
8
PHYSICS
wave
LETTERS
17 April
Table 1 percentage dipole (DS) and quadrupole (QS) strengths T = 1, lliw particle-hole states in 32s.
functions,
for
the JT = l-
Hole
2s;
Id+
Id;
2s;
lP+
Id;
2s;
IdI
lP$
part
2P_‘2
2P$
lf;
2P;
Id;
2P;
lf+
If+
Id{
9.6
11.6
11.9
12.1
13.9
14.4
14.5
16.8
20.1
EO
E 11.2 13.4 14.0 14.8
1967
and 2-,
DS(%) 0.96 -0.08 0.02 -0.16
-0.26
0.10
0.01
-0.02
-0.01
0.0
-0.07
0.62
0.76
0.20
-0.01
-0.02
0.6
-0.28
0.72
-0.61
0.01
-0.00
0.68
-0.15
0.66
-0.62
17.4
0.21
0.68
-0.03
-0.29 0.09
1D
0.16
0.03
1.9
0.19
0.10
13.9
0.12
0.13
65.2
18.3
0.02
0.08
-0.06
0.09
-0.13
0.86
24.0
0.01
0.02
-0.02
0.11
-0.24
0.42
0.86
BSO (%)
6.6
16.1
4.0
4.2
55.1
11.4
35.6
-0.47
2.5 15.9
QS (%) 11.0
0.97
0.21
0.06
0.01
0.03
0.01
0.03
0.02
12.8
0.03
0.38
0.92
0.05
0.13
0.00
0.02
0.01
0.0
13.5
0.20
0.87
0.35
0.16
0.18
0.09
0.08
0.03
34.4
15.0
0.02
0.03
0.03
0.65
0.08
0.76
0.04
0.00
0.1
15.6
0.06
0.08
0.17
0.04
0.96
0.13
0.12
0.00
15.5
16.1
0.06
0.20
0.06
0.73
0.11
0.61
0.19
0.03
11.7
17.9
0.04
0.04
0.02
0.12
0.09
0.15
0.94
0.26
12.3
21.5
0.03
0.03
0 .oo
0.06
0.01
0.06
0.25
0.96
23.8
8.2
0.5
QS, (%)
8.2
37.1
2 B
but one should note that the corresponding states, especially the 2’ state, are now generally considerably lower in energy. The 17.4 and 18.3 MeV levels are in close agreement with the 17.6 and 18.2 MeV levels observed in several (y, n) and (p, 36) experiments [14-171. The 24 MeV level is in agreement with the 24 MeV level observed by Bolen and Whitehead [17] while the 14.8 MeV level may well correspond to the 15 MeV level observed by Dearnaley et al. [16]. Additional major peaks observed by these experiments exists at 19.7, 21.2, 22.8 and 25 MeV. Although the energy level agreement between experiments is good, the relative amplitude of the levels is not. The present calculation indicates that the dipole strength is concentrated at about 17.5 MeV. This is supported by some of the experiments, while others indicate that the strength is concentrated at about 20 MeV. Kossanyi-Demay and Vanpraet [18] have performed the 180 degree inelastic electron scattering ex-
13.3
0.0
17.7
2.2
15.0
periment for a single beam energy of 51 MeV, q N 80 MeV/c , About 15 peaks were observed between about 10 and 28 MeV, many of which agree well with the photoabsorption experiments mentioned above. The peak amplitude of the resonances observed in this range do not vary by more than about 30 percent. In particular, no strong peaks are observed which would indicate the influence of the 24 MeV, l- level and 13.5 MeV, 2level predicted in this calculation. It is hoped that future experiments at higher momentum transfers will be performed. Identical calculations were carried out for 28Si where the unperturbed energy spectrum was taken from Bolen and Eisenberg [7]. Results for the energy levels and wave functions are in reasonable agreement with the l- calculations of Farris and Eisenberg [9]. Seaborn and Eisenberg [ 191 have calculated the E 1 matrix elements and show that the 26 MeV level in 28Si is strongly dominant for momentum transfers above 50 MeV/c 365
Volume
24B, number 8
PHYSICS
LETTERS
17 April
1967
r
2a
4
(MEV/O
Fig.2. Squared, reduced matrix elements for inelastic electron scattering at 180’ from the JB = 2- particlehole states in 32~.
2. G. E. Brown, L. Castillejo 3. q(MEV/'Zi
4. Fig. 1, Squared, reduced matrix elements for inelastic electron scattering at 180’ from the Jr = l- particlehole states in 32~.
5. 6.
as in the present
329 results. Our calculations for 23Si verify this El behaviour and also show a very strong, again rather low-lying (14.3 MeV), M2 element in this high momentum transfer regime. authors would like to thank Mr. S. A. Farris, Prof. J.M. Eisenberg, Dr. P. Kossanyi-Demay, Dr. G. J.Vanpraet, and Prof. W. C. Barber for furnishing their results in advance of publication . The
References
1. G.E.Brown (1959) 472.
366
and M.Bolsterli,
Phys.
Rev.
Letters
3
7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
and J.A. Evans, Nucl. Phys. 22 (1961) 1. F.H.Lewis and J.D.Walecka, Phys. Rev. 133 (1964) B 849. N.Vinh-Mau and G.E.Brown, Nucl. Phys. 29 (1962) 89. V. V. Balashov, V.G.Shevchenko and N. P. Yudin, Nucl. Phys. 27 (1961) 323. L.J.Weigert and J.M.Eisenberg, Nucl. Phys. 53 (1964) 508. L.N.Bolen and J.M.Eisenberg, Phys. Rev. Letters 9 (1964) 52. B. M.Spicer, Au&. J. Phys. 18 (1965) 1. S.A.Farris and d.M.Eisenberg, private communication. P.M.Endt and C.Van der Leun, Nucl. Phys. 34 (1962) 1. P.W.M.Glaudermans et al., Nucl. Phys. 56 (1964) 548 B.C.Carlson and LTalmi, Phys. Rev. 96 (1954) 436. R.Willey, Nucl. Phys. 40 (1963) 529. M.Kimura et al., J. Phys. Sot. Japan 18 (1963) 477. F.W.K.Firk, NucL. Phys. 52 (1964) 437. G.Dearnaley et al., Nucl. Phys. 64 (1965) 177. L.N.Bolen and W.D.Whitehead, Phys. Rev. 132 (1963) 2251. P, Kossanyi-Demay and G. Vanpraet, private communication. J.B.Seaborn and J.M.Eisenberg, Nucl. Phys. 63 (1965) 496.