- Email: [email protected]
Measurement of the alpha particle decay width of the first 0+, T = 2 state in 40Ca
Volume 183, number 1
PHYSICS LETTERS B
1 January 1987
MEASUREMENT OF THE ALPHA PARTICLE DECAY WIDTH O F T H E F I R S T 0 +, T - - 2 S T A T E I N 4°Ca
S.K.B. HESMONDHALGH
1, E.F.
GARMAN, D.M. PRINGLE, S.H. CHEW 2,
W.N. C A T F O R D 3 and K.W. A L L E N Nuclear Physics Laboratory, University of Oxford, Oxford OX1 3RH, UK
Received 19 August 1986
The alpha decay width and total width of the first 0+, T = 2 state in 40Ca have been measured by the elastic scattering of a-particles from 36At. The results are Pa0 = 80 ± 10 eV and F = 81 ± 10 eV.
The decays o f T = 2 states in even-even nuclei in the sd-shell have been studied in detail because o f the evidence they provide for isospin mixing, isospin selection rules and possible limitations on the charge independence o f nuclear forces within nuclei [1,2]. In this letter we report some new results on the particle decay o f the first 0 +, T = 2 state in 40Ca. This state, with an excitation energy o f 11 988 + 2 keV [3], was first observed in the isospin allowed 42Ca(p, t) reaction [1,2]. It was shown to decay primarily by a-particle emission and the branching ratio was measured to be P a o / P = 0.93 + 0.09 [2]. The gamma decay o f this state, excited as a resonance in the reaction 36At(a, 3,)40Ca, was subsequently studied [3] ; two strong M1 transitions to 1+, T = 1 levels at 10.321 MeV and 9.868 MeV were found. There was also evidence for a small proton width to the first excited state o f 39K. The gamma decay studies [3] were carried out by our group using the Oxford windowless cryo-pumped gas target [4]. This target consists o f a 9 cm long stainless steel tube with insulated nozzles at each end. Two helium cryosurfaces provide differential pumping and the target gas is used and recovered many times during an experiment. The aim of the experiment rea Present address: KVI, 9747 AA Groningen, The Netherlands. 2 Present address: PA Computers and Telecommunications, 33 Greycoat Street, London SWl, UK. 3 Present address: Department of Nuclear Physics, ANU, GPO Box 4, Canberra, ACT 2601, Australia. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ported here was to determine the particle widths o f the 0 +, T = 2 state and therefore some rriodifications to the target chamber were required to permit the detection o f protons and elastically scattered a-particles as well as 3,-rays. The major experimental difficulties were expected to arise from the high level density in 4°Ca at ~--12 MeV excitation (average level spacing --~8 keV [5]) and the anticipated small width ( 2 1 0 to 100 eV , x ) of the doubly isospin forbidden decay o f the T = 2 state to 36Ar + % . The high resolution and low background obtainable with our gas target reduced these difficulties and made the experiment feasible. To allow charged particles to escape from the target, a 3 cm long window was set into theside o f the target tube and covered with a thin (1/am) aluminized mylar foil. The arrangement o f the detectors around the target is shown in fig. 1. The 3,-ray detector was 12 X 15 cm NaI crystal. Two litres ofisotopically separated (99.6%) 36At were available for the experiments. A 10/aA beam o f 5.5 MeV He + particles from the Oxford folded tandem accelerator (terminal ion source mode) was used. The beam was stopped 3 cm beyond the target in a shielded, water cooled, Faraday cup. The measurements were performed at a stabilized target pressure of 13 Pa (100 prn o f rig) o f 36Ar. At this pressure the energy loss of the beam in the target was approximately 0.1 keV/cm. Only the central 2 - 3 cm ,1 Lower limit from ref. [3]. Upper limit from observed tend of widths in this mass region, see e.g. ref. [2]. 35
Volume 183, number 1
PHYSICS LETTERS B
1 January 1987
Cryosurface
Charged particle defectors <
Infermediote temperature shield
~
J Target tube
/
Beam
~
I
I:~:,:~:!~ii:i~'r .::~)i ~:!~!~!i !~..~:!;!.::!:-~!~;;-;:t ~:..~:. ,,:::: :~,m
[_I . . . .
q
Shietded
I
= Forodoy cup
~~..~ detector
3.t+ am diameter insuttifed nozzle
Window Target gtls
Fig. 1. Experimental arrangement of the gas target and Ge(Li) and silicon detectors.
region was visible to the collimated charged particle detectors, so the energy loss in the active region was 200-300 eV. Yield curves of 7-rays and elastically scattered ~particles were collected as a function of a-particle bombarding energy. An automatic scanning technique was developed to minimize the effects of any small changes in the experimental conditions. The energy of the beam was varied in steps of 0.2 keV by changing, under computer control, the current in a set of independently powered auxiliary coils in the 90 ° analyzing magnet of the accelerator. The collection of a preset charge on the Faraday cup, typically 5 × 10 -4 Coulomb, determined the dwell time (250 s) at each current setting. The data were recorded in event by event mode on magnetic tape. Each event was described by three parameters; these identified which of the four detectors had fired (three silicon charged particle detectors and one 7-ray detector), how much energy was deposited in the detector, and the energy of the ion beam for the event. The yield of the 2.12 MeV primary 7-ray from the decay of the 0+ , T = 2 state in 40Ca to the 1+, T = 1 state at 10.32 MeV, as shown in fig. 2,was used to 36
2.5[ S-" 2.0 1 1.s
Ex=281/+keY {{ {
1.o I{ {I
"; 2.
!
"
3-
÷
{{
{{{I,
I{
0+, T=2~;
'
{
1.51
15/+a~__~oL5d9o'
E~,=.2120key ssoo Ea(keV)
551o
5~z0
Fig. 2. Gamma ray yield curves.for the 0 +, T = 2 and 3-, T = 0 states in 4OCa showing the 2 keV separation (for details, see text). The other peaks are consistent with gamma decays from the 11 981 and 12 000 keV levels seen by
Nakashima. identify the position of the 0 +, T = 2 state [3]. A 7" ray with an energy of 2.814 MeV, which is equal to
Volume 183, number 1
PHYSICS LETTERSB
the excitation of the second excited state of 39K, was found to resonate at a beam energy 2 keV above that of the T = 2 resonance (see fig. 2). The work of Nakashima [5], who studied resonances in the 39K(p, a)36Ar reaction, suggests that this 7-ray is due to the decay of a 3 - state. These two states are clearly resolved in the 7-ray yield curve, but the yields of elastically scattered a-particles are expected to overlap due to interference effects between resonant and potential scattering. Two of the charged particle detectors were set at 90 ° and 140 ° respectively in the centre-of-mass frame (zeroes of the L = 3 Legendre polynomials) in order to reduce the contribution of the 3 - state; the third detector was set a~ 68 °. A few scattered protons were observed as well as a-particles, but the yield was too small for significant studies. The elastic scattering data were analyzed with Rmatrix theory. The differential centre-of-mass cross section, in the one-level approximation, for the scattering of spin zero particles by spin zero nuclei is, according to Lane and Thomas [6],
1 January 1987
compilation by Percy and Percy [7] were tried and the computer code DWUCK4 [8] was used to extract the phase shifts appropriate to each potential. The parameter sets were very similar and the results of our study were insensitive at the 0.1% level to the values ofnonresonant phase shifts. The matrix element corresponding to a resonant /-value has an additional dispersion term:
Ut = UO + i exp [2i(6o/+ GI) ] E - ' E r - W / 2 ' where E r is the resonance excitation energy and E is the excitation energy. For the analysis of this experiment, there are two closely spaced levels, with 0+, T = 2 and 3 - assignments whose resonant effects have to be included. Since the levels have different spins and parities, it is possible simply to include resonant dispersion terms in the l = 0 and l = 3 collision matrix elements as there are no cross terms. The yield observed per unit (centre of mass) solid angle per incident alpha particle for a beam with an average energy E b may be written as:
f¢; 1
Y(O,Eb) = n
0
+ 2=~ 1=01 (2l + 1 ) [ U / - exp(2i~l)]Pl(COS O)
da
,
.
~-~ (O,E)g(E i ,Eb)
0 0
x where 1 r/cosec 2 (~.) x0 exp I-it/2 In sin(½0)] ~ f(O) = - x/~'~ In these expressions, 6ol is the phase shift due to pure Coulomb scattering and is given by l exp(2i~l) =s~=l= s-iTs + iT
with r~ = ZZ'e2 /hv, the Coulomb parameter. The Ul are the elements of the collision matrix. For nonresonant/-values, they have the form V~ = exp [2i(6o/+ Gl + ff/)], where Gl and I l are the real and imaginary nuclear phase shifts. DWBA formalism was used to generate the nonresonant phase shifts from optical model potentials. Four different sets of potential parameters for the 36At + a system at similar energies from the
where g(E[, Eb) represents the probability that an incident particle has energy E[ when the beam has a nominal energy o r e b ; ¢o(E;, E, x) represents the probability that a particle of incident energy E i' has an energy E at a distance x through a target of length t, n is the target thickness in nuclei/m 3 , and d e / d ~ is the differential cross section discussed above. In order to fit the above expression to experimental data, it is necessary to know the distribution of energies in the incoming beam and in the beam as it traverses the gas target. The energy distribution of the incoming beam was assumed to be gaussian with an energy spread (FWHM) of 1.0 keV [9] at 5.5 MeV and the distribution in the target was obtained by the energy loss parameterization method of Symons [10] developed for our gas target. A least squares fitting programme which could vary up to seven free parameters was written [11] to enable widths to be extracted from the a-particle yield 37
Volume 183, number 1
PHYSICS LETTERS B
f I
~
I
I
3.5
(a)
3.0
~,i+,, . ~+++++++ TTT~ TTtt~{}{'
0CM= 140 °
2.5 2.0
I
i
IIltxl.rt.~?_.
t
x~.~.
zzzzTzT?zT'r~TT'T,~
OCM= ~1.0
I
90° I
(b)
(c)
Ocs = 140 °
Ocs = 140 °
I
i
~Z.O
-~ 1.5
1 January 1987
I
I
L
I
I
I
OcM = 90"
I
I
I
I
f
I
OCM= 90° I
I
iit
24 e~M = 68 °
20
I
I
5490
5495
OCM = 68*
L 5500
I
I
• 5505 %90
I
OcM = I
5 4 9 5 5500 E~(keV)
I
I
5505 %90
68° I
l
%95
5500
,
I
5505
Fig, 3. Yield curves for elastically scattered a-particles in the region ot 12 MeV in 40Ca at three different scattering angles. Tile solid lines are the best fits to the experimental points using the analysis described in the text. Fit (a) is for the 3- state only; fit (b) is for the 0+ state only; fit (c) includes contributions from both the 0+ and 3- states. curves. The principal free parameters were the energies, alpha widths and total widths o f the resonant states. A first attempt to fit the data was made assuming that the only resonant contribution was from the 3 - state. The results o f this analysis are shown in fig. 3a and it is clear that the f i t i s not satisfactory. A second analysis was carried out including a resonant contribution from the 0 + , T = 2 state alone b u t this is equally unsatisfactory; see fig. 3b. However, b y including resonant contributions from b o t h states, good fits were obtained at all three angles as may be seen in fig. 3c. The data for each angle were analyzed independently and the results for the individual angles were combined to form error weighted estimates o f the widths. The variation in extracted widths between: different angles was a maximum o f 4% for the 0 + , T = 2 state and 10% for the 3 - ' state. During the fitting process, the energy spread o f the incident ion beam was allowed to vary from its expected value b y a factor o f two, b u t it was found that the final values o f the widths extracted were unaffected. The excitation energy o f the 0 + , T = 2 state was fixed at the value published in ref. [3]. The separation o f the 3 - and 0 +, T = 2 states was 38
determined from the fit to be 2.0 + 0_5 keV which i s i n agreement with our gamma yield curve data. The 3 - state was found to have a total w i d t h o f 1.28. + 0.23 keV and an alpha width o f 0.110 + 0.015 keV. The best estimate for the total width o f the 0 ÷, T = 2 state was found to be I" = 81 + 10 eV and for the alpha width, Fao = 80 + 10 eV: Values, or limits, for the strengths o f the possible decay modes o f the 0 +, T "= 2 state are shown in table 1. The relative reduced width for a 0-decay o f the 0 + , T = 2 state is
02 = 72/"[LL
=
410 + 51 X 10 - 6 ,
where 72 = P~o/2P (P is the penetrability for a-particle emission) and 7 2 L = 2fi2//aR 2 (g is reduced mass and R is a radius parameter). The Wigner limit 7 2 L and the penetrability were calculated for a radius o f 6.84 fro. This is the largest doubly isospin-forbidden reduced a-particle width known in the (sd) shell [12]. It can be assumed that the a-width arises from isotensor mixing with 0 + , T = 0 states o f similar structure to the 0 +, T = 2 state. The absence o f a significant proton width suggests admixtures o f T = 1 states are small, A schematic calculation taking account o f the admix-
Volume 183, number 1
PHYSICS LETTERS B
Table 1 Decay widths of the 0+, T = 2 state at 11.988 MeV in 40Ca (in eV). r
81 + 10
Pao
80 _+10
Fal
<0.06 [3]
rp0
<4 [21
rpl
0.37 + 0.08 [3]
PP2
<0.012 [3]
rp3
<0.008 [3]
r~
0.78 +- 0.18 a)
a) Calculated from results of ref. [3] and weighted average of r~/F = 0.93 ± 0.09 [2] and 0.99 -+ 0.18 (present experiment).
tures o f various 0 +, T = 0 configurations into the 0 +, T = 2 state (assuming it has a two particle, two hole configuration) has been performed by McGrath et al. [1]. This leads to 0 2 "" 100 X 10 - 6 which is in fair agreement with our result. A more precise calculation requires accurate knowledge of the energies and widths o f the admixing state, especially o f the 0 +, T = 0 two particle, two hole configuration. I t is a pleasure to acknowledge the assistance o f Mr. T. Brock in the design o f the beam energy modu-
1 January 1987
lator and o f Mr. H.R.McK. Hyder and the operators for the maintenance o f the very high quality beams needed for this experiment.
References [1] R.L. McGrath, J. Cerny, J.C. Hardy, G. Goth and A. Arima, Phys. Rev. C 1 (1970) 184. [2] S.J. Freedman, C.A. Galgardi, M.A. Oothoudt, A.V. Nero, R.G.H. Robe.rtson, F.J. Zutavern, E.G. Adelbe~ger and A.B. McDonald, Phys. Rev. C 19 (1979) 1907. [3] D.M. Pringle, E.F. Garman, S.H. Chew, K.A. Snorer, W.N. Cafford, S.K.B. Hesmondhalgh and K.W. Alien, Phys. Lett. B 115 (1982) 291. [4] F. Watt, L.K. Fifield, M.J. Hurst, T.J.M. Symons, C.H. Zimmerman and K.W. Allen, Nucl. Instrum. Methods 151 (1978) 163. [5] T. Nakashima, J. Phys. Soc. Japan 36 (1974) 10. [6] A.M. Lane and R.G. Thomas, Rev. Mod. Phys. 30 (1958) 257. [7] C.M, Percy and F.G. Percy, At. Dat. NucL Dat. Tab. 17 (1976) 1. [8] P.D. Kunz, University of Colorado (1974), unpunished, [9] W.N, Catford, D. Phil. thesis, University of Oxford (1981), unpublished. [10] T.J.M. Symons, L.K. Fifield, M.J. Hurst, F. Watt, C.H. Zimmerman and K.W. Allen, J. Phys. G 4 (1978) 411, [ 11] S.K.B. Hesmondhalgh, D. Phil. thesis, University of Oxford ( 1985), unpublished. [ 12] A.B. McDonald, E.D. Earle, W. McLatchie, H.B. Mak, D.J. Martin and P.S. Ikossi, Nuel. Phys. A 305 (1978) 151.
39
PHYSICS LETTERS B
1 January 1987
MEASUREMENT OF THE ALPHA PARTICLE DECAY WIDTH O F T H E F I R S T 0 +, T - - 2 S T A T E I N 4°Ca
S.K.B. HESMONDHALGH
1, E.F.
GARMAN, D.M. PRINGLE, S.H. CHEW 2,
W.N. C A T F O R D 3 and K.W. A L L E N Nuclear Physics Laboratory, University of Oxford, Oxford OX1 3RH, UK
Received 19 August 1986
The alpha decay width and total width of the first 0+, T = 2 state in 40Ca have been measured by the elastic scattering of a-particles from 36At. The results are Pa0 = 80 ± 10 eV and F = 81 ± 10 eV.
The decays o f T = 2 states in even-even nuclei in the sd-shell have been studied in detail because o f the evidence they provide for isospin mixing, isospin selection rules and possible limitations on the charge independence o f nuclear forces within nuclei [1,2]. In this letter we report some new results on the particle decay o f the first 0 +, T = 2 state in 40Ca. This state, with an excitation energy o f 11 988 + 2 keV [3], was first observed in the isospin allowed 42Ca(p, t) reaction [1,2]. It was shown to decay primarily by a-particle emission and the branching ratio was measured to be P a o / P = 0.93 + 0.09 [2]. The gamma decay o f this state, excited as a resonance in the reaction 36At(a, 3,)40Ca, was subsequently studied [3] ; two strong M1 transitions to 1+, T = 1 levels at 10.321 MeV and 9.868 MeV were found. There was also evidence for a small proton width to the first excited state o f 39K. The gamma decay studies [3] were carried out by our group using the Oxford windowless cryo-pumped gas target [4]. This target consists o f a 9 cm long stainless steel tube with insulated nozzles at each end. Two helium cryosurfaces provide differential pumping and the target gas is used and recovered many times during an experiment. The aim of the experiment rea Present address: KVI, 9747 AA Groningen, The Netherlands. 2 Present address: PA Computers and Telecommunications, 33 Greycoat Street, London SWl, UK. 3 Present address: Department of Nuclear Physics, ANU, GPO Box 4, Canberra, ACT 2601, Australia. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ported here was to determine the particle widths o f the 0 +, T = 2 state and therefore some rriodifications to the target chamber were required to permit the detection o f protons and elastically scattered a-particles as well as 3,-rays. The major experimental difficulties were expected to arise from the high level density in 4°Ca at ~--12 MeV excitation (average level spacing --~8 keV [5]) and the anticipated small width ( 2 1 0 to 100 eV , x ) of the doubly isospin forbidden decay o f the T = 2 state to 36Ar + % . The high resolution and low background obtainable with our gas target reduced these difficulties and made the experiment feasible. To allow charged particles to escape from the target, a 3 cm long window was set into theside o f the target tube and covered with a thin (1/am) aluminized mylar foil. The arrangement o f the detectors around the target is shown in fig. 1. The 3,-ray detector was 12 X 15 cm NaI crystal. Two litres ofisotopically separated (99.6%) 36At were available for the experiments. A 10/aA beam o f 5.5 MeV He + particles from the Oxford folded tandem accelerator (terminal ion source mode) was used. The beam was stopped 3 cm beyond the target in a shielded, water cooled, Faraday cup. The measurements were performed at a stabilized target pressure of 13 Pa (100 prn o f rig) o f 36Ar. At this pressure the energy loss of the beam in the target was approximately 0.1 keV/cm. Only the central 2 - 3 cm ,1 Lower limit from ref. [3]. Upper limit from observed tend of widths in this mass region, see e.g. ref. [2]. 35
Volume 183, number 1
PHYSICS LETTERS B
1 January 1987
Cryosurface
Charged particle defectors <
Infermediote temperature shield
~
J Target tube
/
Beam
~
I
I:~:,:~:!~ii:i~'r .::~)i ~:!~!~!i !~..~:!;!.::!:-~!~;;-;:t ~:..~:. ,,:::: :~,m
[_I . . . .
q
Shietded
I
= Forodoy cup
~~..~ detector
3.t+ am diameter insuttifed nozzle
Window Target gtls
Fig. 1. Experimental arrangement of the gas target and Ge(Li) and silicon detectors.
region was visible to the collimated charged particle detectors, so the energy loss in the active region was 200-300 eV. Yield curves of 7-rays and elastically scattered ~particles were collected as a function of a-particle bombarding energy. An automatic scanning technique was developed to minimize the effects of any small changes in the experimental conditions. The energy of the beam was varied in steps of 0.2 keV by changing, under computer control, the current in a set of independently powered auxiliary coils in the 90 ° analyzing magnet of the accelerator. The collection of a preset charge on the Faraday cup, typically 5 × 10 -4 Coulomb, determined the dwell time (250 s) at each current setting. The data were recorded in event by event mode on magnetic tape. Each event was described by three parameters; these identified which of the four detectors had fired (three silicon charged particle detectors and one 7-ray detector), how much energy was deposited in the detector, and the energy of the ion beam for the event. The yield of the 2.12 MeV primary 7-ray from the decay of the 0+ , T = 2 state in 40Ca to the 1+, T = 1 state at 10.32 MeV, as shown in fig. 2,was used to 36
2.5[ S-" 2.0 1 1.s
Ex=281/+keY {{ {
1.o I{ {I
"; 2.
!
"
3-
÷
{{
{{{I,
I{
0+, T=2~;
'
{
1.51
15/+a~__~oL5d9o'
E~,=.2120key ssoo Ea(keV)
551o
5~z0
Fig. 2. Gamma ray yield curves.for the 0 +, T = 2 and 3-, T = 0 states in 4OCa showing the 2 keV separation (for details, see text). The other peaks are consistent with gamma decays from the 11 981 and 12 000 keV levels seen by
Nakashima. identify the position of the 0 +, T = 2 state [3]. A 7" ray with an energy of 2.814 MeV, which is equal to
Volume 183, number 1
PHYSICS LETTERSB
the excitation of the second excited state of 39K, was found to resonate at a beam energy 2 keV above that of the T = 2 resonance (see fig. 2). The work of Nakashima [5], who studied resonances in the 39K(p, a)36Ar reaction, suggests that this 7-ray is due to the decay of a 3 - state. These two states are clearly resolved in the 7-ray yield curve, but the yields of elastically scattered a-particles are expected to overlap due to interference effects between resonant and potential scattering. Two of the charged particle detectors were set at 90 ° and 140 ° respectively in the centre-of-mass frame (zeroes of the L = 3 Legendre polynomials) in order to reduce the contribution of the 3 - state; the third detector was set a~ 68 °. A few scattered protons were observed as well as a-particles, but the yield was too small for significant studies. The elastic scattering data were analyzed with Rmatrix theory. The differential centre-of-mass cross section, in the one-level approximation, for the scattering of spin zero particles by spin zero nuclei is, according to Lane and Thomas [6],
1 January 1987
compilation by Percy and Percy [7] were tried and the computer code DWUCK4 [8] was used to extract the phase shifts appropriate to each potential. The parameter sets were very similar and the results of our study were insensitive at the 0.1% level to the values ofnonresonant phase shifts. The matrix element corresponding to a resonant /-value has an additional dispersion term:
Ut = UO + i exp [2i(6o/+ GI) ] E - ' E r - W / 2 ' where E r is the resonance excitation energy and E is the excitation energy. For the analysis of this experiment, there are two closely spaced levels, with 0+, T = 2 and 3 - assignments whose resonant effects have to be included. Since the levels have different spins and parities, it is possible simply to include resonant dispersion terms in the l = 0 and l = 3 collision matrix elements as there are no cross terms. The yield observed per unit (centre of mass) solid angle per incident alpha particle for a beam with an average energy E b may be written as:
f¢; 1
Y(O,Eb) = n
0
+ 2=~ 1=01 (2l + 1 ) [ U / - exp(2i~l)]Pl(COS O)
da
,
.
~-~ (O,E)g(E i ,Eb)
0 0
x where 1 r/cosec 2 (~.) x0 exp I-it/2 In sin(½0)] ~ f(O) = - x/~'~ In these expressions, 6ol is the phase shift due to pure Coulomb scattering and is given by l exp(2i~l) =s~=l= s-iTs + iT
with r~ = ZZ'e2 /hv, the Coulomb parameter. The Ul are the elements of the collision matrix. For nonresonant/-values, they have the form V~ = exp [2i(6o/+ Gl + ff/)], where Gl and I l are the real and imaginary nuclear phase shifts. DWBA formalism was used to generate the nonresonant phase shifts from optical model potentials. Four different sets of potential parameters for the 36At + a system at similar energies from the
where g(E[, Eb) represents the probability that an incident particle has energy E[ when the beam has a nominal energy o r e b ; ¢o(E;, E, x) represents the probability that a particle of incident energy E i' has an energy E at a distance x through a target of length t, n is the target thickness in nuclei/m 3 , and d e / d ~ is the differential cross section discussed above. In order to fit the above expression to experimental data, it is necessary to know the distribution of energies in the incoming beam and in the beam as it traverses the gas target. The energy distribution of the incoming beam was assumed to be gaussian with an energy spread (FWHM) of 1.0 keV [9] at 5.5 MeV and the distribution in the target was obtained by the energy loss parameterization method of Symons [10] developed for our gas target. A least squares fitting programme which could vary up to seven free parameters was written [11] to enable widths to be extracted from the a-particle yield 37
Volume 183, number 1
PHYSICS LETTERS B
f I
~
I
I
3.5
(a)
3.0
~,i+,, . ~+++++++ TTT~ TTtt~{}{'
0CM= 140 °
2.5 2.0
I
i
IIltxl.rt.~?_.
t
x~.~.
zzzzTzT?zT'r~TT'T,~
OCM= ~1.0
I
90° I
(b)
(c)
Ocs = 140 °
Ocs = 140 °
I
i
~Z.O
-~ 1.5
1 January 1987
I
I
L
I
I
I
OcM = 90"
I
I
I
I
f
I
OCM= 90° I
I
iit
24 e~M = 68 °
20
I
I
5490
5495
OCM = 68*
L 5500
I
I
• 5505 %90
I
OcM = I
5 4 9 5 5500 E~(keV)
I
I
5505 %90
68° I
l
%95
5500
,
I
5505
Fig, 3. Yield curves for elastically scattered a-particles in the region ot 12 MeV in 40Ca at three different scattering angles. Tile solid lines are the best fits to the experimental points using the analysis described in the text. Fit (a) is for the 3- state only; fit (b) is for the 0+ state only; fit (c) includes contributions from both the 0+ and 3- states. curves. The principal free parameters were the energies, alpha widths and total widths o f the resonant states. A first attempt to fit the data was made assuming that the only resonant contribution was from the 3 - state. The results o f this analysis are shown in fig. 3a and it is clear that the f i t i s not satisfactory. A second analysis was carried out including a resonant contribution from the 0 + , T = 2 state alone b u t this is equally unsatisfactory; see fig. 3b. However, b y including resonant contributions from b o t h states, good fits were obtained at all three angles as may be seen in fig. 3c. The data for each angle were analyzed independently and the results for the individual angles were combined to form error weighted estimates o f the widths. The variation in extracted widths between: different angles was a maximum o f 4% for the 0 + , T = 2 state and 10% for the 3 - ' state. During the fitting process, the energy spread o f the incident ion beam was allowed to vary from its expected value b y a factor o f two, b u t it was found that the final values o f the widths extracted were unaffected. The excitation energy o f the 0 + , T = 2 state was fixed at the value published in ref. [3]. The separation o f the 3 - and 0 +, T = 2 states was 38
determined from the fit to be 2.0 + 0_5 keV which i s i n agreement with our gamma yield curve data. The 3 - state was found to have a total w i d t h o f 1.28. + 0.23 keV and an alpha width o f 0.110 + 0.015 keV. The best estimate for the total width o f the 0 ÷, T = 2 state was found to be I" = 81 + 10 eV and for the alpha width, Fao = 80 + 10 eV: Values, or limits, for the strengths o f the possible decay modes o f the 0 +, T "= 2 state are shown in table 1. The relative reduced width for a 0-decay o f the 0 + , T = 2 state is
02 = 72/"[LL
=
410 + 51 X 10 - 6 ,
where 72 = P~o/2P (P is the penetrability for a-particle emission) and 7 2 L = 2fi2//aR 2 (g is reduced mass and R is a radius parameter). The Wigner limit 7 2 L and the penetrability were calculated for a radius o f 6.84 fro. This is the largest doubly isospin-forbidden reduced a-particle width known in the (sd) shell [12]. It can be assumed that the a-width arises from isotensor mixing with 0 + , T = 0 states o f similar structure to the 0 +, T = 2 state. The absence o f a significant proton width suggests admixtures o f T = 1 states are small, A schematic calculation taking account o f the admix-
Volume 183, number 1
PHYSICS LETTERS B
Table 1 Decay widths of the 0+, T = 2 state at 11.988 MeV in 40Ca (in eV). r
81 + 10
Pao
80 _+10
Fal
<0.06 [3]
rp0
<4 [21
rpl
0.37 + 0.08 [3]
PP2
<0.012 [3]
rp3
<0.008 [3]
r~
0.78 +- 0.18 a)
a) Calculated from results of ref. [3] and weighted average of r~/F = 0.93 ± 0.09 [2] and 0.99 -+ 0.18 (present experiment).
tures o f various 0 +, T = 0 configurations into the 0 +, T = 2 state (assuming it has a two particle, two hole configuration) has been performed by McGrath et al. [1]. This leads to 0 2 "" 100 X 10 - 6 which is in fair agreement with our result. A more precise calculation requires accurate knowledge of the energies and widths o f the admixing state, especially o f the 0 +, T = 0 two particle, two hole configuration. I t is a pleasure to acknowledge the assistance o f Mr. T. Brock in the design o f the beam energy modu-
1 January 1987
lator and o f Mr. H.R.McK. Hyder and the operators for the maintenance o f the very high quality beams needed for this experiment.
References [1] R.L. McGrath, J. Cerny, J.C. Hardy, G. Goth and A. Arima, Phys. Rev. C 1 (1970) 184. [2] S.J. Freedman, C.A. Galgardi, M.A. Oothoudt, A.V. Nero, R.G.H. Robe.rtson, F.J. Zutavern, E.G. Adelbe~ger and A.B. McDonald, Phys. Rev. C 19 (1979) 1907. [3] D.M. Pringle, E.F. Garman, S.H. Chew, K.A. Snorer, W.N. Cafford, S.K.B. Hesmondhalgh and K.W. Alien, Phys. Lett. B 115 (1982) 291. [4] F. Watt, L.K. Fifield, M.J. Hurst, T.J.M. Symons, C.H. Zimmerman and K.W. Allen, Nucl. Instrum. Methods 151 (1978) 163. [5] T. Nakashima, J. Phys. Soc. Japan 36 (1974) 10. [6] A.M. Lane and R.G. Thomas, Rev. Mod. Phys. 30 (1958) 257. [7] C.M, Percy and F.G. Percy, At. Dat. NucL Dat. Tab. 17 (1976) 1. [8] P.D. Kunz, University of Colorado (1974), unpunished, [9] W.N, Catford, D. Phil. thesis, University of Oxford (1981), unpublished. [10] T.J.M. Symons, L.K. Fifield, M.J. Hurst, F. Watt, C.H. Zimmerman and K.W. Allen, J. Phys. G 4 (1978) 411, [ 11] S.K.B. Hesmondhalgh, D. Phil. thesis, University of Oxford ( 1985), unpublished. [ 12] A.B. McDonald, E.D. Earle, W. McLatchie, H.B. Mak, D.J. Martin and P.S. Ikossi, Nuel. Phys. A 305 (1978) 151.
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