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Proton-helium total reaction cross sections between 18 and 48 MeV
Volume 51B, number 3
PHYSICS LETTERS
5 August 1974
PROTON-HELIUM TOTAL REACTION CROSS SECTIONS B E T W E E N 18 A N D 48 MeV* A.M. SOURKES, N.E. DAVISON, S.A. ELBAKR, J.L. HORTON*, A. HOUDAYER* and W.T.H. van OERS Cyclotron Laboratory, Department of Physics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
and R.F. CARLSON Department of Physics, University of Redlands, Redlands, California 92373, USA Received 24 June 1974 Proton total reaction cross sections for aHe and 4He have been measured in the energy range 18 to 48 MeV at ten and sixteen energies respectively. Comparison is made with other experimental nucleon-induced reaction information. Comparing the p_4He measurements with phase shift analyses, resonating-groupcalculations, and optical model predictions, points to improvement for the model-dependent theoretical work.
Experimental total reaction cross s e c t i o n (OR) measurements on very light nuclear systems are important for fundamental few-nucleon calculations where only a small number of adjustable parameters are involved (e.g., two parameter resonating-group calculations [1,2] ). Moreover, o R measurements can be used to distinguish among various final phase shift solutions and to determine the accuracy of the imaginary potential in optical model analyses. The lack of o R information for p-3He, until now, has hampered theoretical development in that area while the small amount of accurate p-4He data has not permitted an adequate evaluation of the existing theoretical predictions [e.g. 1] for that system. Thus, a program of o R measurements at energies between 18 and 48 MeV~t, using protons from the University of Manitoba cyclotron in conjunction with a beam attenuation measurement apparatus [3], was undertaken to provide OR data for p-He at many energies including a number at which theoretical predictions exist. A variant of the standard low-energy attenuation technique was used [3]. The target was a finite length Work supported in part by the Atomic Energy Control Board of Canada and by the Research Corporation. * Present address: Radiation Laboratory, Aberdeen Proving Grounds, Aberdeen, Maryland 21005, USA. * Present address: Foster Radiation Laboratory, McGiU University, Montreal, Quebec, Canada. :~ All energies refer to laboratory proton reaction energies. 232
gas cell pressurized to approximately 20 atm. The experimental procedure consisted of determining the inelastic attenuation of a proton beam incident on the helium gas target. This was accomplished by a single measurement giving the inelastic attenuation of the incident beam within a forward cone, and the inelastic plus elastic attenuation outside this cone. The attenuation due to the gas cell windows was determined in a separate measurement on the evacuated cell and subsequently subtracted. The elastic attenuation to be subtracted from the total attenuation was calculated using available elastic scattering data. This correction term was obtained by dividing the five centimeter long gas cell into fifty geometrically well-defined segments and treating each one separately. Corrections were then made for reaction products counted as non-attenuation events, elastically scattered protons counted as attenuation events and for energy-dependent scattering effects of the cell exit foil. The overall error contributions resuited from a 2% uncertainty in the elastic scattering correction term, a I% measurement error, estimated from the reproducibility of the total attenuation cross section, and a 1% uncertainty contributed by the other correction terms. FoUowing the method suggested by Bichsel [4], an energy calibration of the bending magnet located upstream from the total reaction cross section apparatus was made using four measurements spanning the energy range 20 to 50 MeV. Accurately lapped Si absorbers
Volume 51B, number 3
200 E Z o_ 1.50 I-
i
i
PHYSICS LETTERS I
EE
I
I
5 August 1974
II1°
i
'
-= 150 E
L
Z kI.)
,oo
'
I
I
• ,z, o ~ IO0 z
_o B
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z o 5O I.u
R ~ THRESHOLDS § PRESENT p-4He WORK a RESONATINGGROUPTHEDRY[I]
w II;
• PHASES . ~ RESU,TS[~3l • | I x °
p-:SHe REFERENCE [6]
~-0
n-3He REFERENCE [7] (3- AND 4-BODY SUM)
I Q.
I
I 20
i
g
o o
REAC'RON THRESHOLDS - ~t PRESENT p-aHe WORK
I I0
'
l
30
t
l
40
,
l
50
-
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,
I 30
,
PHASE SHIFT RESULTS [14] p-4He REFERENCE [10] p-4He REFERENCE [I I] DETAILED BAL. RESULTS [12] OPT. MOOELPREI~CnONSD6] "
I 40
,
I
,
5O
T~a(MeV)
T~8(MeV)
Fig. 1. Present p-aHe total reaction cross sections compared with other nucleon-induced results.
Fig. 2. Present p-4He total reaction cross sections compared with other o R determinations. The 15% uncertainty in the detailed balance values for oR is not shown.
were used to degrade the proton beam energy. The degraded energy was determined by comparison with 241Am and ThC source lines. The incident proton energy was then calculated using Si range energy tables accurate to better than 0.2% [5]. This allowed an overall calibration accuracy of -+100 keV. The o R result for p-3He are shown in fig. 1. Experimental data deduced from the work of Griffiths and Harbison [6] are also displayed in the figure. These o R results were obtained by adding integrations of the 3- and 4-body channels from 90 ° to 180 ° in the center of mass to the results reported in table 2 of ref. [6]. The sum of the 3- and 4-body n-3He reaction channel cross sections between 7.9 and 23.7 MeV inferred by Drosg et al. [7] are also included for comparison. The present o R results for p-3He make the extension of phase shift analyses (such as that of Morales-Pena [8] ) to include imaginary phases, more feasible. In addition, inclusion of an imaginary potential in the p+3He resonating-group calculations ofref. [9] becomes possible [2], The present experimental o R results for p-4He are shown in fig. 2 along with the result of Cairnes et al. [10] and the estimates of Hayakawa et al. [11]. Also included are the detailed balance o R values based on the 3He(d, p)4He work of Yarnell et al. [12]. Fig. 2 presents as well, predictions from resonating-group cal-
culations in the one channel approximation [ 1], and predictions from the phase shift analysis of Plattner et al. [13] up to 40 MeV and from the extension of this analysis to 50 MeV by Houdayer and van Oers [14] The two experimental results shown below the 23.2 MeV reaction threshold are consistent with an expected null value. The detailed balance values exhibit reasonable agreement with the present work below 24.9 MeV where 4He(p, d)3He is the only reaction channel open. The sharp dip across the 23.4 MeV resonance (corresponding to the second excited state in 5Li at 16.65 MeV excitation) displayed by the phase shift predictions and detailed balance trR values, is not observed in the present experiment due to 150 keV incident beam energy spread and 375 keV target thickness. It should be noted that in the phase shift analysis of Plattner et al. the Yarnell results were used as a constraint, so that below 25 MeV the phase shifts were determined with the criterion of agreeing with the detailed balance values for o R. The phase shift o R predictions [13] continue to agree with the present work up to their 40 MeV limit. Between 40 and 50 MeV the o R predictions from the work of Houdayer and van Oers [14] also show good agreement. In the latter analysis, however, the o R data were used to distinguish among various final phase shift solutions. The 233
Volume 51B, number 3
PHYSICS LETTERS
o R predictions from resonating-group theory calculations [1] which used estimates o f o R at a f e w energies only, show a reasonable energy dependence thought the values are uniformly low. Explicit coupled-channel treatment by resonating-group theory o f the p+a elastic and d+3He reaction channels [15] reproduces the features o f the angular dependence o f the reaction channel at 85 MeV. However, the magnitude o f the predicted reaction-channel cross section is again somewhat low. Thompson, Epstein and Sawada [16] in their 30 to 55 MeV p-4He optical model analysis obtained reasonable o R values o f about 95 mb (fig. 2) but only at a sacrifice in the fits to the elastic scatterhag data. Their best fit parameters yielded o R values near 150 mb. A recent optical model calculation at 85 MeV using an/-dependent optical potential [17], although fitting the elastic scattering data very well, still appears to over-estimate the total reaction cross section. In summary, the o R results for p-3He provide information enabling extension of the theoretical treatment of this system. The o R results for p-4He indicate the need for further refinement in the model-dependent calculations*. The authors would like to express thanks to Mark de Jong, John Nimmo, James Rae and Mike Wright for * The data are available in tabular form from the authors on request.
234
5 August 1974
their aid in experimental equipment set up and data collection.
References [I] D.R. Thompson, Y.C. Tang and R.E. Brown, Phys. Rev. C5 (1972) 1939. [2] R.E. Brown, private communication. [3] R.F. Carlson et al., to be published. [4] H. Bichsel, private communication. [5] H. Biehsel and C. Tschalaer, Nuclear Data A3 (1967) 343. [6] R.J. Griffiths and S.A. Harbison, Astr. J. 158 (1969) 711. [7] M. Drosg et al., Phys. Rev. C9 (1974) 179. [8] J.R. Morales-Pena, Ph.D. thesis, University of California at Davis (1970), unpublished. [9] I. Reichstein, D.R. Thompson and Y.C. Tang, Phys. Rev. C3 (1971) 2139. [10] D.J. Cairns et al., Nud. Phys. 60 (1964) 369. [11] S. Hayakawa et al., J. Phys. Soc. Japan 19 (1964) 2004. [12] J.L. YarneU, R.H. Lovberg and W.R. Stratton, Phys. Rev. 90 (1953) 292. [13] G.R. Plattner, A.D. Bacher and H.E. Conzett, Phys. Rev. C5 (1972) 1158. [14] A. Houdayer and W.T.H. van Oers, private communication. [15] F.S. Chwieroth, Y.C. Tang and D.R. Thompson, Phys. Rev. C9 (1974) 56. [16] G.E. Thompson, M.B. Epstein and T. Sawada, Nucl. Phys. A142 (1970) 571. [17] L.G. Votta, P.G. Roos, N.S. Chant and R. Woody, University of Maryland, Rep 74-011 (1973) unpublished.
PHYSICS LETTERS
5 August 1974
PROTON-HELIUM TOTAL REACTION CROSS SECTIONS B E T W E E N 18 A N D 48 MeV* A.M. SOURKES, N.E. DAVISON, S.A. ELBAKR, J.L. HORTON*, A. HOUDAYER* and W.T.H. van OERS Cyclotron Laboratory, Department of Physics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
and R.F. CARLSON Department of Physics, University of Redlands, Redlands, California 92373, USA Received 24 June 1974 Proton total reaction cross sections for aHe and 4He have been measured in the energy range 18 to 48 MeV at ten and sixteen energies respectively. Comparison is made with other experimental nucleon-induced reaction information. Comparing the p_4He measurements with phase shift analyses, resonating-groupcalculations, and optical model predictions, points to improvement for the model-dependent theoretical work.
Experimental total reaction cross s e c t i o n (OR) measurements on very light nuclear systems are important for fundamental few-nucleon calculations where only a small number of adjustable parameters are involved (e.g., two parameter resonating-group calculations [1,2] ). Moreover, o R measurements can be used to distinguish among various final phase shift solutions and to determine the accuracy of the imaginary potential in optical model analyses. The lack of o R information for p-3He, until now, has hampered theoretical development in that area while the small amount of accurate p-4He data has not permitted an adequate evaluation of the existing theoretical predictions [e.g. 1] for that system. Thus, a program of o R measurements at energies between 18 and 48 MeV~t, using protons from the University of Manitoba cyclotron in conjunction with a beam attenuation measurement apparatus [3], was undertaken to provide OR data for p-He at many energies including a number at which theoretical predictions exist. A variant of the standard low-energy attenuation technique was used [3]. The target was a finite length Work supported in part by the Atomic Energy Control Board of Canada and by the Research Corporation. * Present address: Radiation Laboratory, Aberdeen Proving Grounds, Aberdeen, Maryland 21005, USA. * Present address: Foster Radiation Laboratory, McGiU University, Montreal, Quebec, Canada. :~ All energies refer to laboratory proton reaction energies. 232
gas cell pressurized to approximately 20 atm. The experimental procedure consisted of determining the inelastic attenuation of a proton beam incident on the helium gas target. This was accomplished by a single measurement giving the inelastic attenuation of the incident beam within a forward cone, and the inelastic plus elastic attenuation outside this cone. The attenuation due to the gas cell windows was determined in a separate measurement on the evacuated cell and subsequently subtracted. The elastic attenuation to be subtracted from the total attenuation was calculated using available elastic scattering data. This correction term was obtained by dividing the five centimeter long gas cell into fifty geometrically well-defined segments and treating each one separately. Corrections were then made for reaction products counted as non-attenuation events, elastically scattered protons counted as attenuation events and for energy-dependent scattering effects of the cell exit foil. The overall error contributions resuited from a 2% uncertainty in the elastic scattering correction term, a I% measurement error, estimated from the reproducibility of the total attenuation cross section, and a 1% uncertainty contributed by the other correction terms. FoUowing the method suggested by Bichsel [4], an energy calibration of the bending magnet located upstream from the total reaction cross section apparatus was made using four measurements spanning the energy range 20 to 50 MeV. Accurately lapped Si absorbers
Volume 51B, number 3
200 E Z o_ 1.50 I-
i
i
PHYSICS LETTERS I
EE
I
I
5 August 1974
II1°
i
'
-= 150 E
L
Z kI.)
,oo
'
I
I
• ,z, o ~ IO0 z
_o B
t
t
z o 5O I.u
R ~ THRESHOLDS § PRESENT p-4He WORK a RESONATINGGROUPTHEDRY[I]
w II;
• PHASES . ~ RESU,TS[~3l • | I x °
p-:SHe REFERENCE [6]
~-0
n-3He REFERENCE [7] (3- AND 4-BODY SUM)
I Q.
I
I 20
i
g
o o
REAC'RON THRESHOLDS - ~t PRESENT p-aHe WORK
I I0
'
l
30
t
l
40
,
l
50
-
"1,q. I
I 2O
,
I 30
,
PHASE SHIFT RESULTS [14] p-4He REFERENCE [10] p-4He REFERENCE [I I] DETAILED BAL. RESULTS [12] OPT. MOOELPREI~CnONSD6] "
I 40
,
I
,
5O
T~a(MeV)
T~8(MeV)
Fig. 1. Present p-aHe total reaction cross sections compared with other nucleon-induced results.
Fig. 2. Present p-4He total reaction cross sections compared with other o R determinations. The 15% uncertainty in the detailed balance values for oR is not shown.
were used to degrade the proton beam energy. The degraded energy was determined by comparison with 241Am and ThC source lines. The incident proton energy was then calculated using Si range energy tables accurate to better than 0.2% [5]. This allowed an overall calibration accuracy of -+100 keV. The o R result for p-3He are shown in fig. 1. Experimental data deduced from the work of Griffiths and Harbison [6] are also displayed in the figure. These o R results were obtained by adding integrations of the 3- and 4-body channels from 90 ° to 180 ° in the center of mass to the results reported in table 2 of ref. [6]. The sum of the 3- and 4-body n-3He reaction channel cross sections between 7.9 and 23.7 MeV inferred by Drosg et al. [7] are also included for comparison. The present o R results for p-3He make the extension of phase shift analyses (such as that of Morales-Pena [8] ) to include imaginary phases, more feasible. In addition, inclusion of an imaginary potential in the p+3He resonating-group calculations ofref. [9] becomes possible [2], The present experimental o R results for p-4He are shown in fig. 2 along with the result of Cairnes et al. [10] and the estimates of Hayakawa et al. [11]. Also included are the detailed balance o R values based on the 3He(d, p)4He work of Yarnell et al. [12]. Fig. 2 presents as well, predictions from resonating-group cal-
culations in the one channel approximation [ 1], and predictions from the phase shift analysis of Plattner et al. [13] up to 40 MeV and from the extension of this analysis to 50 MeV by Houdayer and van Oers [14] The two experimental results shown below the 23.2 MeV reaction threshold are consistent with an expected null value. The detailed balance values exhibit reasonable agreement with the present work below 24.9 MeV where 4He(p, d)3He is the only reaction channel open. The sharp dip across the 23.4 MeV resonance (corresponding to the second excited state in 5Li at 16.65 MeV excitation) displayed by the phase shift predictions and detailed balance trR values, is not observed in the present experiment due to 150 keV incident beam energy spread and 375 keV target thickness. It should be noted that in the phase shift analysis of Plattner et al. the Yarnell results were used as a constraint, so that below 25 MeV the phase shifts were determined with the criterion of agreeing with the detailed balance values for o R. The phase shift o R predictions [13] continue to agree with the present work up to their 40 MeV limit. Between 40 and 50 MeV the o R predictions from the work of Houdayer and van Oers [14] also show good agreement. In the latter analysis, however, the o R data were used to distinguish among various final phase shift solutions. The 233
Volume 51B, number 3
PHYSICS LETTERS
o R predictions from resonating-group theory calculations [1] which used estimates o f o R at a f e w energies only, show a reasonable energy dependence thought the values are uniformly low. Explicit coupled-channel treatment by resonating-group theory o f the p+a elastic and d+3He reaction channels [15] reproduces the features o f the angular dependence o f the reaction channel at 85 MeV. However, the magnitude o f the predicted reaction-channel cross section is again somewhat low. Thompson, Epstein and Sawada [16] in their 30 to 55 MeV p-4He optical model analysis obtained reasonable o R values o f about 95 mb (fig. 2) but only at a sacrifice in the fits to the elastic scatterhag data. Their best fit parameters yielded o R values near 150 mb. A recent optical model calculation at 85 MeV using an/-dependent optical potential [17], although fitting the elastic scattering data very well, still appears to over-estimate the total reaction cross section. In summary, the o R results for p-3He provide information enabling extension of the theoretical treatment of this system. The o R results for p-4He indicate the need for further refinement in the model-dependent calculations*. The authors would like to express thanks to Mark de Jong, John Nimmo, James Rae and Mike Wright for * The data are available in tabular form from the authors on request.
234
5 August 1974
their aid in experimental equipment set up and data collection.
References [I] D.R. Thompson, Y.C. Tang and R.E. Brown, Phys. Rev. C5 (1972) 1939. [2] R.E. Brown, private communication. [3] R.F. Carlson et al., to be published. [4] H. Bichsel, private communication. [5] H. Biehsel and C. Tschalaer, Nuclear Data A3 (1967) 343. [6] R.J. Griffiths and S.A. Harbison, Astr. J. 158 (1969) 711. [7] M. Drosg et al., Phys. Rev. C9 (1974) 179. [8] J.R. Morales-Pena, Ph.D. thesis, University of California at Davis (1970), unpublished. [9] I. Reichstein, D.R. Thompson and Y.C. Tang, Phys. Rev. C3 (1971) 2139. [10] D.J. Cairns et al., Nud. Phys. 60 (1964) 369. [11] S. Hayakawa et al., J. Phys. Soc. Japan 19 (1964) 2004. [12] J.L. YarneU, R.H. Lovberg and W.R. Stratton, Phys. Rev. 90 (1953) 292. [13] G.R. Plattner, A.D. Bacher and H.E. Conzett, Phys. Rev. C5 (1972) 1158. [14] A. Houdayer and W.T.H. van Oers, private communication. [15] F.S. Chwieroth, Y.C. Tang and D.R. Thompson, Phys. Rev. C9 (1974) 56. [16] G.E. Thompson, M.B. Epstein and T. Sawada, Nucl. Phys. A142 (1970) 571. [17] L.G. Votta, P.G. Roos, N.S. Chant and R. Woody, University of Maryland, Rep 74-011 (1973) unpublished.