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Energy determination of heavy-ion beams
N U C L E A R I N S T R U M E N T S AND METHODS
161 (19791
1 7 3 - 1 8 2 ; (~) N O R T H - H O L L A N D PUBLISHING CO.
:i
ENERGY DETERMINATION OF HEAVY-ION BEAMS* H. P. TRAUTVETTER, K. ELIX and C. ROLFS
Instiut .for Kernphysik, Universiti~t Miinster, Fed. Rep. Germany and K. BRAND
Dynamitron-Tandem-Laboratorium, Ruhr-Universitiit Bochum, Fed. Rep. Germany Received 14 November 1978 The energy calibration of the beam analyzing magnet at the 4 MV Dynamitron tandem accelerator in Bochum has been carried out over a wide magnetic field range (B= 2.4-12.4 k G / u s i n g the well-known energies of several proton induced resonance reactions. The roles of projectile and target nuclei have been exchanged in these reactions, i.e. a hydrogen gas target has been bombarded with the corresponding heavy ions. In this way, the necessary high energies of the heavy ion beams were accurately defined and used in the calibration of the beam analyzing magnet at high field strengths. For the field range investigated, the magnet calibration factor K was observed to be constant within experimental uncertainties (AK=_+0.2%). Atomic effects in the measurement of nuclear energies are discussed.
1. Introduction
The investigation of nuclear reactions relevant to the field of nuclear astrophysics often requires I) a precise knowledge of the absolute beam energy. This requirement is of special importance at projectile energies far below the Coulomb barrier, where the reaction cross sections drop quickly with decreasing beam energy. The absolute energy of an ion beam is most commonly determined by an analyzing magnet, which must be calibrated e.g. using the energies of certain known resonances or threshold energies. Lists of recommended calibration energies are readily available 2) and many examples of such calibration procedures as well as new methods involving non-resonant proton capture reactions can be found in the literature 3 6). The most precise calibration energies 2,61 involve proton induced reactions at Ep = 0.3-3.5 MeV. At higher proton energies, the use of (p, n) threshold energies ( E p = 4 . 2 - 9 . 5 M e V ) is recommended2), however, these energies are not as precisely known. In addition, the normal neutron background at these high proton energies tends to be large and to obscure the relatively weak neutron yield at threshold. Therefore, the energy calibration of the magnetic analyzer is most commonly carried out with low-energy proton induced reactions. The deduced calibration parameters relate Supported in part by the Deutsche Forschungsgemeinschaft, Fed. Rep. Germany (Ro 429/2-5).
the proton beam energies to a limited range of field strengths of the magnetic analyzer. For heavy-ion beams, however, the magnetic fields required are usually far removed from the calibrated field range. Consequently, an absolute energy determination for these beams depends heavily on the extrapolation procedure of the calibration parameters towards high magnetic field strengths. This procedure is usually not verified by experiments and the absolute beam energies of heavy ions are therefore not known with high precision. The well-known proton induced reactions at Er_<3.5 MeV can, however, be used to calibrate accurately the magnetic analyzer at high field strengths, if the roles of projectile and target nuclei are reversed, i.e. if a hydrogen gas target is bombarded by the corresponding energetic heavy ions. Using several different charge states of the heavy-ion beam, the same resonance can, in principle, lead to several calibration points over a wide range of magnetic field strengths. For the astrophysical research program involving heavy ion beams as well as for other heavy ion research activities at the high-current 4 MV Dynamitron tandem accelerator in Bochum, the beam analyzing magnet has been calibrated over nearly the full range of field strengths using beams of protons and heavy ions (~3C and 19F). The experimental equipment and set-up are described in section 2. The description of the experimental procedures, data analyses a n d results follows in section 3.
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TRAUTVETTER
2. Experimental equipment and set-up The 4 MV Dynamitron tandem accelerator at Bochum provided beams of protons, ~3C- and 19Fions (table 1) using a modified version of the Middleton sputtering ion sourceT). The rather unusual and inexpensive beam handling system consists of three small single focussing "switching" magnets of the same model. One of these magnets is used as the analyzing magnet with output legs at ___52.5° serving each of the two switching magnets. The magnetic field strength of the analyzing magnet is controlled by a nuclear magnetic resonance (NMR) unit using a single probe for the full range of magnetic field strengths. This unit* allows the measurement of absolute magnetic fields with a precision of better than 2 × 10 -5. To compensate for the relatively low resolving power of the analyzing magnet, a high electronic gain has been used for the slit-feedback system. Details of the accelerator, the beam handling system and the beam qualities have been described previouslyS). Following the switching magnet, the beam was guided through the four canals of a windowless, recirculating gas target system consisting of three pumping stages. A schematic diagram of the relevant parts of this system 9) and of the experimental set-up is shown in fig. 1. The disk-shaped tar-
et al.
get chamber has eight channels directed towards the center of the target chamber which are used e.g. for gas recirculation, for pressure and elastic scattering yield measurements and for a viewing window. In this set-up, the electrically insulated Faraday cup is part of the target volume and so the effective target length / has been defined by the heavy lead shielding around the y-ray detector (fig. 1). The walls of the target chamber and the Faraday-cup are lined with Ta sheets. The gas pressure in the target chamber is measured to an accuracy of +_0.01 Torr with a Baratron capacitance manometer*. The accuracy of the manometer has been ascertained by comparison with an absolute standard gaugeg). The gas pressure at several other locations in the gas target system is measured by thermocouple, penning and ionisation manometers~). Typical gas pressures observed in the system are indicated in fig. 1. The y-ray transitions were detected with a 80 cm 3 Ge(Li) detector. The energy resolution of this detector was 2.2 keV at Ey= 1.3 MeV. The detector was placed at a distance of 8 cm from the beam axis and surrounded by a 6 cm thick lead shield (fig. 1). The effective target length / as well as the distance d from the midpoint of the entrance canal A to the center of the target chamber (fig. 1) were determined by moving a 22Na source
* Model 5200 of Cyclotron Corporation, Berkeley, U.S.A.
* Model 221 HS100 from MKS I n s t r u m e n t s .
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Fig. 1. Schematic diagram o f the relevant parts o f the windowless, recirculating gas target s y s t e m 9) and o f the experimental set-up. The diameters and distances o f the four canals as well as the observed pressure reduction in the gas target s y s t e m are indicated. The disk-shaped target c h a m b e r 9) is followed by an electrically insulated, watercooled Faraday cup. The Ge(Li) detector is s u r r o u n d e d by a heavy lead shielding, which defines the effective target length in the target chamber. A Si particle detector (not shown), installed at 120 ° in the target c h a m b e r , is used to m o n i t o r the beam intensity during the runs.
ENERGY
DETERMINATION
along
the beam axis [d = (10.3 ___0.2) cm, 1.27 M e V ) = (9.5_+0.2) cm]. Due to the lead shielding and solid angle effects of the Ge(Li) detector, the effective target length / depends on 7ray energy. Since normal charge measurements at the Faraday-cup are not reliable due to charge-exchange effects of the projectile ions in the gas target, the use of a Si particle detector was necessary to observe the elastically scattered projectiles from the gas target nuclei and thereby to monitor the beam intensity in the measurement of resonance yield curves. A Si particle detector of the ruggedized type was placed at an angle of 120° with respect to the beam axis and collimated by a 0.32 mm wide horizontal slit placed near the beam axis together with a 4 mm O aperture in front of the detector (fig. 2 of ref. 9). Standard signal amplifying and analyzing equipment was used in conjunction with both detectors.
I(Ey =
3. Experimental procedures, data analyses and results 3.1. CHOICE OF CALIBRATION ENERGIES In order to calibrate the beam analyzing magnet over a wide range of field strengths (2.4-12.4 kG), suitable resonance reactions had to be selected according to the following requirements: (i) wellknown resonance energy; (ii) large y-ray yield and, if possible, small total width; (iii) sufficient beam
OF H E A V Y - I O N
175
BEAMS
intensity from the sputtering ion source; (iv) sufficient intensity for the selected charge state of the heavy ion beam with respect to the available high voltage range (0.5-4.0 MV) of the accelerator; (v) availability of the required target nuclei as gases and (vi) distribution of calibration points over the full range of magnetic field strengths in approximately equal steps. These requirements are fairly well fulfilled for the reactions listed in table 1. 3.2. TARGET GASES AND GAS MIXTURES For the measurement of resonance yield curves, the beam intensity in the gas target was monitored by the intensity of the elastically scattered projectiles at 120° backward angle (section 2). Since the total widths of the 13C(p,~')IaN and Z°Ne(p, y)2~Na resonances are rather small (table 1), the elastic scattering yield is, for the target pressures used (table 2), not influenced by interference effects between Coulomb and resonance scattering over the energy region of the resonance. For the broader IaN(p, ~')lsO resonances, however, such effects are expected and therefore the beam intensity was monitored by the elastic scattering yield from Xe nuclei, admixed into the target gas (table 2). The same technique has been applied in the case of the heavy-ion induced reactions on hydrogen target nuclei, since the elastic scattering of heavy-ions from hydrogen target nuclei is only possible in the forward direction. Table 2 summar-
TABLE 1 Resonance reactions, absolute beam energies and charge states of the projectiles and stopping powers of the gas targets. Case Nr. 1 2 3 4 5 6 7 8
Reaction :~
2°Ne(p, 7)2J Na 13C(p, y)14N 2° Ne(p, p'y)2°Ne 14N(p, 7)150 14N(p, y)lsO p(13C, y)14N b p(19F, ~y)16OC p(19F, ~y)16od
Proton-beam e Elab (keV) Fla 0 (keV) 1168.8_+0.8 1747.6_+0.9 1955.0_+2.0 2479.0+ 1.7 4203.0±3.0
Heavy-ion beam f Eub (keV) Fl~b (keV)
(15.5_+1.4)10 -3 (77 ±12)10 -3 3.93±0.10 9.4_+0.5 43±4 22548.2_+11.8 16440.0_+ 5.2 6418.0_+ 1.3
1.0_+0.2 89_+4 45±4
Charge state g
Stopping power h (keV mm I T o r r - 1 )
1 1 1 1 1 5 4 2
0.01998 0.04108 0.01530 0.02244 0.01557 0.5603 1.4111 1.5484
Listed according to increasing magnetic field strengths (B0 =2.4-12.4 kG, table 3). Identical to case nr. 2 in the cm-system. Corresponding2) to Ep (lab) = (872.11 ±0.20)keV [Fla b = (4.7±0.2)keV]. Corresponding 2 ) to Ep (lab) = (340.46 ± 0.04) keV [ Flab = (2.4 ± 0.2)keV]. Refs. 2, 10 and 11. Calculated values from reported proton-induced data 2) using exact masses]°, J3). The errors include the uncertainties in the proton-induced resonance energies and in the relevant masses. g Beam currents of up to 2, 0.3 and 10/IA were used for protons, 13C- and 19F-ions, respectively. h Stopping powers from ref. 12 for the target gas mixtures used (table 2) assume a gas temperature of 20°C. b c d e r
H.P.
176
TRAUTVETTER
et al.
izes the target gases and gas mixtures as well as the total pressures of the gas mixtures employed in the experiments. The H2, N2 and Xe gases were chemically pure to better than one part in 10 -5 . The CO2 gas* was enriched to 90% in ~3C. Although natural neon gas predominantly consists of the isotope 2°Ne (90.5%), the isotope 22Ne (9.2%) produces intense resonances via the 22Ne(p, y)23Na reaction in the same beam energy region. For this reason, enriched 2°Ne gas* (99.95%) was employed in the experiment.
"FABLE
3.3. MEASUREMENT OF RESONANCE YIELD CURVES
a Chemically pure gases ( < 1 0 ppm) with natural isotopic abundances. b Enriched to 90% in 13C. c Enriched to 99.95% in 2°Ne.
The resonance yield curves were deduced from the dominant y-ray transitions in the reaction of interest. Sample y-ray spectra accumulated at the Ecru = 1613 keV resonance of 13C(p, ~')laN and * Monsanto Corporation, Miamisburg, USA.
2
Target gases, gas mixtures and total gas pressures. Reaction
p(13C, y)14 N 13C(p, y)14 N 14N(p, y)t50
2ONe(p ' y)21Na p(19F, aty)16 O
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p(13C, )')14N are shown in fig. 2. Theintensity. of the dominant R--,0 (79%) y-ray decay ~l) is normalized to the 120 ° elastic scattering yield of the
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NUMBER Fig. 2. Sample y-ray spectra obtained with the Oe(Li) detector at the Ecm=1613keV resonance of the 13C+p compound nucleus using (a) a proton and (c) a ]3C beam. The high y-ray background observed with the 13C-beam arises predominantly from i2C + 13C reactions of the beam with traces of carbon contaminations on the canals, walls of the target chamber and beam stop (fig. 1). Parts (b) and (d) illustrate the associated particle spectra obtained from the elastic scattering of protons and 13C-ions by the 13CO2 and H 2 + X e gas target mixtures, respectively. These spectra were used to monitor the beam intensity during the runs.
ENERGY DETERMINATION OF HEAVY-ION BEAMS
projectiles. The measurement of the yield curves for both reactions have been carried out at several target gas pressures and the results are illustrated in fig. 3a and b. The yield curve results obtained for the other resonance reactions (table 1) are summarized in fig. 4. After a particular resonance (table 1) had been located, the following precautions were taken prior to the final yield curve measurements: (i) in order to prevent differential hysteresis effects of the analyzing magnet, the magnet was recycled in a procedure similar to that described in ref. 3; (ii) the beam transmission through the gas target system (fig. 1) was optimized at each step in beam energy by maximizing the beam current measured in the Faraday-cup without gas in the target chamber. Nearly full beam transmission was achieved. It should be noted, that reduction of target gas pressure along the beam axis due to space-charge repulsion and hard collisions is not important at the target pressures (up to 5 Tort) and beam currents employed. This feature has been verified experimentally at the E~,b=6418 keV resonance of the p(19F, o:'y)160 reaction using 19F2+ beam currents of 4 and 19~A (fig. 41). 3.4. SHAPE OF THE YIELD CURVES Due to the extended gas target (fig. 1), the location of a given resonance moves along the beam axis as the beam energy is varied. Furthermore, the heavy lead shield around the Ge(Li) y-ray detector defines an effective target length / along the beam axis, where the resonance can be detected (fig. 1). If the target thickness A over this length / is much larger than the resonance width F(A >> 1-3 and if the y-ray detection efficiency is uniform within this effective detection window, the observed y-ray yield curve would be a rectangular step function. The front edge of this function will have, however, a finite slope due to the action of the following effects: (i) the finite resonance width F, (ii) the finite beam energy resolution ~, (iii) the beam energy straggling between the entrance canal A and the beginning of the effective target length /, (iv) the y-ray absorption effects at the edge of the lead collimator and (v) the variation of the solid angle of the detector as seen from the beam axis over the edge of the effective target length. The back edge of this yield curve function should then exhibit the mirror shape of the front edge except that the additional beam en-
177
ergy straggling along the target length / should further decrease the slope of this edge. If the above effects are symmetric in beam energy, the edges of the yield curves should have a shape very similar to the thick-target yield curve of a narrow resonance. Since the efficiency and solid angle of the y-ray detector vary only slightly within the effective target length l, the top of the yield curve is expected to be fiat. This flat top as well as the finite slopes at the front and back edges of the yield curves are indeed observed for target pressures corresponding to the condition A>> F (figs. 3a, 3b and 4a). The observed slopes at the edges of these yield curves originate predominantly from beam energy straggling in the gas target and to a lesser degree by the other effects mentioned above. In the other extreme case, i.e. A <~F, the yield curve should reflect a normal greit-Wigner shape with a width r/ corresponding to the quadratic addition of the resonance width F and the beam energy resolution ~. Intermediate cases can be constructed by folding the Breit-Wigner shape with the profile of the detection efficiency (for a given y-ray energy) in the present set-up (fig. 1). It should be noted that the y-ray yield curves for different gas target pressures have been normalized to the same number of elastically scattered projectiles. Since this number is directly proportional to the gas pressure, the fiat top of the y-ray yield curves should decrease in proportion to the target pressure used if, for all pressures used, the condition A >> F applies. This feature is fairly well fulfilled in the investigations of the E~ab=22548keV resonance of the p(13C, y)laN reaction (fig. 4a and table 1). 3.5. ANALYSIS PROCEDURES
The analysis procedures used in calibrating the magnetic analyzer are illustrated by the example of the E~o = 22 548 keV resonance of p(13C, }')I4N (table 1). The yield curves obtained for target pressures of p = l . 0 , 3.0 and 5.0Torr are shown in fig. 3a. Due to the small total resonance width of Flab = (1.0--+0.2)keV (table 1), the observed widths zl of these yields curves (defined by the midpoints at the front and back edges) are predominantly due to the energy loss of the beam over the effective target length /. The observed width e.g. of A ~ 158 keY for a pressure of 3.0 Torr (fig. 3a) is in excellent agreement with the calculated value of A = 1 6 0 k e V using / = 9 . 5 c m and the stopping
178
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Fig. 3. Resonance 7-ray yield curves For the 13C + p reaction obtained with a 13C (a) and proton (b) beam at different target gas pressures. The central energy shifts as well as the decreasing widths of the curves as a function of target chamber pressure are due to the energy loss of the beam over the distances d and I, respectively (fig. l). The lines through the data points are to guide the eye. The central points of the yield curves for the |3C beam (a) are shown in part (c) as a Function of gas pressure v e r s u s the magnetic field squared.
ENERGY
DETERMINATION
OF H E A V Y - I O N
power value e of table 1 for p = 3.0 Torr. The central point of these yield curves is defined by the half distance between the midpoints of the edges. Since these edges are observed to be nearly symmetrical, this definition insures that the central point is the energy corresponding to the location of the resonance at the center of the target chain•
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ERes=1.169MeV E~ : 3.5LMeV
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179
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Fig. 4. Resonance 7-ray yield curves for p r o t o n - i n d u c e d resonances on 2°Ne (a and b) and 14N (c and d) gas targets. The yield curves for the ]9F-beam on a h y d r o g e n gas target are s h o w n in (e) and (f). The pressures used and the 7-ray energy range analysed are indicated for each reaction. Part (f) d e m o n s t r a t e s that different beam current loads in the gas target do not affect significantly the location o f the central points o f the yield curves. Due to pile-up effects in the y-ray detector at this intense resonance, the 7-ray yield on top o f the resonance is higher at the lower beam currents. The lines through the data points are to guide the eye.
180
H.P.
T R A U T V E T T E R et al.
fields) with decreasing target gas pressure, in accord with observation (fig. 3a). The observed energy of the resonance. ER(P), at the center of the target chamber is therefore related to the true resonance energy E0 (i.e. for an infinite thin target) by the equation ER(P) = E o + A E ( p )
TABLE 3 Results for magnetic field strength and magnet calibration factor. Case nr.
Magnetic field B0 a (G)
Magnet calibration factor K b (G/MeV)
= E o + d~p,
where e is the energy loss in the target gas (table 1). If the central energy E R is plotted as a function of target pressure p, the slope of this straight line is proportional to de and hence the value of e can be determined experimentally. For the H2-Xe gas mixture (tables 1 and 2), the shifts of the yield curve central energies (fig. 3a) result in a stopping power of e=(0.557_+0.014)keV mm 1Torr ~ For a gas temperature of 20°C, the tables of Northcliffe and Schilling 12) lead to a value of e = 0.5603 keV mm I Torr -1 (table 1), in good agreement with the above experimental value. If the magnetic field strength squared B~ (p), corresponding to the central resonance energy E R(p), is plotted versus the target pressure, the extrapolation to " z e r o " pressure ~ leads to the relevant value of B~. For the above resonance, this procedure yields (fig. 3c) a value of B0 = (7692.6_+0.4)G (table 3). In the analyses of the yield curves obtained for all the other resonance reactions, the tables of ref. 12 were used in the determination of the beam energy loss (table 1) over the distance d in the target chamber. The resulting magnetic field strengths B0 are summarized in table 3. The 'following sources of errors were considered for the individual B0-results: a) Statistical error in the central point determination of the yield curves. This error covers also possible asymmetries in the slopes of the front and back edges in the yield curves and is much larger than the uncertainties in the measurement of the absolute magnetic field or in differential hysteresis effects 3) of the analyzing magnet (section 2). b) Due to the rapid pressure reduction (combined with the short distances between the canals) in the gas target system (fig. 1), the energy loss of
Similar procedures in the extrapolation of the front and back edges of the yield curves lead to values of E0 - q/2 and E 0 + q / 2 with r/= v'F2+~ 1. The experiment reveals r/~20 keV, which corresponds to an energy resolution of the 13CS+-beam of ~ < 2 0 k e V .
1 2 3 4 5 6 7 8
2435.9 +_ 0.4 2977.5-+ 1.3 3151.9-+ 0.3 3545.6_+ 2.1 4620.6_+ 1.9 7692.1 _+ 1.3 9914.0+_ 4.2 12373.6_+ 10.9 Weighted average
51.982 -+0.020 51.955_+0.035 51.996-+0.053 51.936_+0.047 51.956+_0.043 52.014+_0.029 51.975-+0.027 51.918+_0.047 51.975 -+0.011 c
a Uncertainties obtained as quadratic addition of the following statistically independent errors: the central point determination of the yield curves, the gas mixing and absolute pressure measurement including effects induced by the beam, the effective length d and the stopping power value ~. b Errors correspond to the quadratic addition of the uncertainties in the magnetic field Bo, the absolute beam energies E0 and the relevant nuclear masses. c Internal error 3) only. The external error 3) is _+0.009.
the beam can be neglected in the gas target system up to the entrance canal A of the target chamber. Assuming that the gas pressure increases linearly within the 1 cm long canal A, the beam equivalently loses energy uniformly from the center of this canal to the center of the target chamber. To this distance of d = 10.3 cm (fig. 1), an error of _+0.7 cm has been assigned to account for the uncertainty of the pressure profile in the canal A (_+0.5 cm) and the position of the Ge(Li) detector within the lead shield (_+0.2 cm). This error is common to all experiments. c) The stopping power values e of ref. 12 were used for a gas temperature of 20°C. The good agreement between the observed and calculated evalues in the case of the p(13C, }')14N experiment (see above) indicates, that temperature effects or changes in gas density along the beam axis in the gas target chamber can be neglected. A 5°C increase in the gas temperature would decrease the e-value by 2% in the above case. Since in this experiment a 13C-beam of only _<50 nA particle current was employed and since such effects are expected to increase with the particle current, the intense t9F beam was used to search for these effects. The results (fig. 4f and section 3.3) reveal that they are negligible ( < 8 % ) for the target pres-
ENERGY
DETERMINATION
sures and particle currents employed. An error in e of _+ 10% has been adopted as a conservative estimate for both these effects and the uncertainties in the tabulated s-values~2). d) Due to an unstable valve in the gas cleaning elements 9) of the gas target system, the gas target pressure could change during the running periods by as much as +0.05 Torr. This uncertainty was common to all experiments. Since all these errors are statistically independent and common to all individual experiments, they have been added quadratically to obtain the total error in the final B0-values (table 3).
OF H E A V Y - I O N
BEAMS
181
w o r k - w i t h a constant calibration factor over the full range of magnetic field strengths, with a weighted average of K = (51.975+0.011) G MeV (table 3). This result implies a precision in the determination of heavy-ion energies of 4 parts in 104 , which is sufficient for all practical purposes of interest (section 1). 3.7. ATOMIC EFFECTS ON NUCLEAR RESONANCE ENERGIES
In the case of nuclear resonance reactions, the nuclear Q-value QN is given by the relation QN = QA + B(Zp) + B(Z,) - B(Z~)
3.6. THE MAGNET CALIBRATION FACTOR
The calibration factor K for the analyzing magnet is defined through the well-known relation 2) K = ZpBo,/\ (2,q%C2Ep +- E~),
where the quantities Zp, mp and Ep a r e the charge state, exact mass and laboratory energy of the projectile, respectively and B0 is the magnetic field of the analyzer. With the values given in tables 1 and 3, the resulting values for the magnet calibration factor K are summarized in table 3 and plotted in fig. 5 as a function of magnetic field strength B0. Since the Z2-fit to the data for a field-independent magnet calibration factor leads to a normalized value of )~2 =0.7, the data are consistent-within the experimental uncertainties of the present
~
>~
52z.
o ~ 522
co
Q~
o d
52o
51 8 GO Proton Becm
13C5 " Beam
19~"* Beam
l
,
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c~
51.6
~ :E
0
l 2
,
l
~
l
4 MAGNETIC
, 6
glELD
~
i 8
l ~ 10
12
14
(kGauss)
Fig. 5. Results for the magnet calibration factor K are plotted as a function of magnetic field strength B 0 (table 3). The line through the data points represents the result of a Z2-fit (Z2=0.7) for a field-independent K = ( 5 1 . 9 7 5 _ 0 . 0 1 1 ) G / M e V . The types of projectile ions used in the calibration of the magnetic analyzer are also indicated.
where QA represents the calculated Q-value on the basis of tabulated atomic masses and the quantities B(Zp), B ( Z ) and B(z~) are the total electronic binding energies of the projectile, target and compound atom, respectively. Since the differences in electronic binding energies between the projectile plus target atoms and the compound atom are small, such atomic effects on nuclear resonance energies can usually be neclegted. The existence of such atomic effects on nuclear resonance energies has been demonstrated however, in the high-precision experiment of StaubU). In the elastic scattering of neutral 4He atoms with singly charged 4He+ ions leading to the groundstate of the compound nucleus 8Be, this nuclear resonance has been observed to be splitting up into several nearby resonances, where the energy differences were consistent with the spacing of the lowest few electronic states of the compound atom 8Be. In the present work, for the calibration of the magnetic analyzer at high field strengths, heavyion beams were used to bombard a hydrogen gas target and the energies of these heavy ions were defined by the well-known (proton induced) resonance energies. If in the formation of the compound nucleus the associated compound atom suffers drastic changes, the nuclear resonance energies can again shift or split up by a sizable amount. The effects will be most significant, if, in the formation of the compound nucleus, electrons from the inner shells of the associated electron cloud are excited or removed. For example, if for the E~ab = 6418 keV resonance of the p(19F, 0c7)160 reaction a K-vacancy is created in the formation of the 2°Ne compound atom, the nuclear mass of 2°Ne will increase by 0.869 keV and consequently
182
H . P . TRAUTVETTER et al.
the laboratory resonance energy should increase by A E v -.~ 0.869 x 19 = 16.5 keV. This increase in nuc-
lear resonance energy would correspond to a change in the magnet calibration factor K by A K = 0.065, which is of the same size as the experimental uncertainty (fig. 5 and table 3). For the other heavy-ion induced resonances, the creation of a K-vacancy in the formation of the c o m p o u n d atom would change the magnet calibration factor by AK(19F)= 0.025 and AK(13C)= 0.006, which is again well within the experimental errors (fig. 5 and table 3). Since the details of such atomic effects on the nuclear resonance energies are poorly understood, corrections due to such effects have been omitted in the energy calibration of the magnetic analyzer. It should be pointed out, however, that the experimental uncertainties in the present equipment and set-up (section 3.5) could in principle be reduced significantly, such that the above and other heavy-ion induced resonance reactions on hydrogen gas targets could be used as a tool to study the atomic effects on nuclear resonance energies in more detail. The K.U. course thank ments
authors acknowledge the help of J. G6rres, Kettner and P. Schmalbrock during the of the experiments. We would like to also Dr. W . E . Kieser for the helpful comon the manuscript. The travel supprt prov-
ided by the Westf~ilische Wilhelms-Universit~it Miinster is highly appreciated.
References 1) c. Rolls and H. P. Trautvetter, Experimental nuclear astrophysics, Ann. Rev. Nucl. Sci. 28 (1978) 115. 2) j. B. Marion, Rev. Mod. Phys. 38 (1966) 660; J. B. Marion and F. C. Young, Nuclear reaction analysis (NorthHolland, Amsterdam, 1968). 3) j. C, Overlay, P. D. Parker and D. A. Bromley, Nucl. Instr. and Meth. 68 (1969) 61. 4) M. L. Roush, L. A. West and J. B. Marion, Nucl. Phys. A147 (1970) 235. 5) C. Rolls, W. S. Rodney, S. Durrance and H. Winkler, Nucl. Phys. A240 (1975) 221. 6) T. Freye, H. Lorenz-Wirzba, B. Cleft, H. P. Trautvetter and C. Rolls, Z. Physik A281 (1977) 211. 7) K. Brand, Nucl. Instr. and Meth. 141 (1977) 519. 8) E. Blanke, K. Brand, H. Genz, A. Richter and G. Schrieder, Nucl. Instr. and Meth. 122 (1974) 295. 9) C. Rolls, J. G6rres, K. U. Kettner, H. Lorenz-Wirzba, P. Schmalbrock, H. P. Trautvetter and W. Verhoeven, Nucl. Instr. and Meth. 157 (1978) 19. 10) p. M. Endt and C. van der Leun, Nucl. Phys. A214 (1973) 1. 11) F. Ajzenberg-Selove, Nucl. Phys. A268 (1976) 1. 12) L. C. Northclifte and R. F. Schilling, Nucl. Data Tables 7 (1970) 233. 13) L. G. Smith and A. H. Wapstra, Phys. Rev. Cll (1975) 1392. 14) H. H. Staub, Proc. Int. Conf. At. Masses, ed. R. C. Barber, (University of Manitoba Press, 1967) p. 495; J. Benn, E. B. Dally, H. H. Miiller, R. E. Pixley, H. H. Staub and H. Winkler, Nucl. Phys. A106 (1968) 296.
161 (19791
1 7 3 - 1 8 2 ; (~) N O R T H - H O L L A N D PUBLISHING CO.
:i
ENERGY DETERMINATION OF HEAVY-ION BEAMS* H. P. TRAUTVETTER, K. ELIX and C. ROLFS
Instiut .for Kernphysik, Universiti~t Miinster, Fed. Rep. Germany and K. BRAND
Dynamitron-Tandem-Laboratorium, Ruhr-Universitiit Bochum, Fed. Rep. Germany Received 14 November 1978 The energy calibration of the beam analyzing magnet at the 4 MV Dynamitron tandem accelerator in Bochum has been carried out over a wide magnetic field range (B= 2.4-12.4 k G / u s i n g the well-known energies of several proton induced resonance reactions. The roles of projectile and target nuclei have been exchanged in these reactions, i.e. a hydrogen gas target has been bombarded with the corresponding heavy ions. In this way, the necessary high energies of the heavy ion beams were accurately defined and used in the calibration of the beam analyzing magnet at high field strengths. For the field range investigated, the magnet calibration factor K was observed to be constant within experimental uncertainties (AK=_+0.2%). Atomic effects in the measurement of nuclear energies are discussed.
1. Introduction
The investigation of nuclear reactions relevant to the field of nuclear astrophysics often requires I) a precise knowledge of the absolute beam energy. This requirement is of special importance at projectile energies far below the Coulomb barrier, where the reaction cross sections drop quickly with decreasing beam energy. The absolute energy of an ion beam is most commonly determined by an analyzing magnet, which must be calibrated e.g. using the energies of certain known resonances or threshold energies. Lists of recommended calibration energies are readily available 2) and many examples of such calibration procedures as well as new methods involving non-resonant proton capture reactions can be found in the literature 3 6). The most precise calibration energies 2,61 involve proton induced reactions at Ep = 0.3-3.5 MeV. At higher proton energies, the use of (p, n) threshold energies ( E p = 4 . 2 - 9 . 5 M e V ) is recommended2), however, these energies are not as precisely known. In addition, the normal neutron background at these high proton energies tends to be large and to obscure the relatively weak neutron yield at threshold. Therefore, the energy calibration of the magnetic analyzer is most commonly carried out with low-energy proton induced reactions. The deduced calibration parameters relate Supported in part by the Deutsche Forschungsgemeinschaft, Fed. Rep. Germany (Ro 429/2-5).
the proton beam energies to a limited range of field strengths of the magnetic analyzer. For heavy-ion beams, however, the magnetic fields required are usually far removed from the calibrated field range. Consequently, an absolute energy determination for these beams depends heavily on the extrapolation procedure of the calibration parameters towards high magnetic field strengths. This procedure is usually not verified by experiments and the absolute beam energies of heavy ions are therefore not known with high precision. The well-known proton induced reactions at Er_<3.5 MeV can, however, be used to calibrate accurately the magnetic analyzer at high field strengths, if the roles of projectile and target nuclei are reversed, i.e. if a hydrogen gas target is bombarded by the corresponding energetic heavy ions. Using several different charge states of the heavy-ion beam, the same resonance can, in principle, lead to several calibration points over a wide range of magnetic field strengths. For the astrophysical research program involving heavy ion beams as well as for other heavy ion research activities at the high-current 4 MV Dynamitron tandem accelerator in Bochum, the beam analyzing magnet has been calibrated over nearly the full range of field strengths using beams of protons and heavy ions (~3C and 19F). The experimental equipment and set-up are described in section 2. The description of the experimental procedures, data analyses a n d results follows in section 3.
174
H.P.
TRAUTVETTER
2. Experimental equipment and set-up The 4 MV Dynamitron tandem accelerator at Bochum provided beams of protons, ~3C- and 19Fions (table 1) using a modified version of the Middleton sputtering ion sourceT). The rather unusual and inexpensive beam handling system consists of three small single focussing "switching" magnets of the same model. One of these magnets is used as the analyzing magnet with output legs at ___52.5° serving each of the two switching magnets. The magnetic field strength of the analyzing magnet is controlled by a nuclear magnetic resonance (NMR) unit using a single probe for the full range of magnetic field strengths. This unit* allows the measurement of absolute magnetic fields with a precision of better than 2 × 10 -5. To compensate for the relatively low resolving power of the analyzing magnet, a high electronic gain has been used for the slit-feedback system. Details of the accelerator, the beam handling system and the beam qualities have been described previouslyS). Following the switching magnet, the beam was guided through the four canals of a windowless, recirculating gas target system consisting of three pumping stages. A schematic diagram of the relevant parts of this system 9) and of the experimental set-up is shown in fig. 1. The disk-shaped tar-
et al.
get chamber has eight channels directed towards the center of the target chamber which are used e.g. for gas recirculation, for pressure and elastic scattering yield measurements and for a viewing window. In this set-up, the electrically insulated Faraday cup is part of the target volume and so the effective target length / has been defined by the heavy lead shielding around the y-ray detector (fig. 1). The walls of the target chamber and the Faraday-cup are lined with Ta sheets. The gas pressure in the target chamber is measured to an accuracy of +_0.01 Torr with a Baratron capacitance manometer*. The accuracy of the manometer has been ascertained by comparison with an absolute standard gaugeg). The gas pressure at several other locations in the gas target system is measured by thermocouple, penning and ionisation manometers~). Typical gas pressures observed in the system are indicated in fig. 1. The y-ray transitions were detected with a 80 cm 3 Ge(Li) detector. The energy resolution of this detector was 2.2 keV at Ey= 1.3 MeV. The detector was placed at a distance of 8 cm from the beam axis and surrounded by a 6 cm thick lead shield (fig. 1). The effective target length / as well as the distance d from the midpoint of the entrance canal A to the center of the target chamber (fig. 1) were determined by moving a 22Na source
* Model 5200 of Cyclotron Corporation, Berkeley, U.S.A.
* Model 221 HS100 from MKS I n s t r u m e n t s .
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Fig. 1. Schematic diagram o f the relevant parts o f the windowless, recirculating gas target s y s t e m 9) and o f the experimental set-up. The diameters and distances o f the four canals as well as the observed pressure reduction in the gas target s y s t e m are indicated. The disk-shaped target c h a m b e r 9) is followed by an electrically insulated, watercooled Faraday cup. The Ge(Li) detector is s u r r o u n d e d by a heavy lead shielding, which defines the effective target length in the target chamber. A Si particle detector (not shown), installed at 120 ° in the target c h a m b e r , is used to m o n i t o r the beam intensity during the runs.
ENERGY
DETERMINATION
along
the beam axis [d = (10.3 ___0.2) cm, 1.27 M e V ) = (9.5_+0.2) cm]. Due to the lead shielding and solid angle effects of the Ge(Li) detector, the effective target length / depends on 7ray energy. Since normal charge measurements at the Faraday-cup are not reliable due to charge-exchange effects of the projectile ions in the gas target, the use of a Si particle detector was necessary to observe the elastically scattered projectiles from the gas target nuclei and thereby to monitor the beam intensity in the measurement of resonance yield curves. A Si particle detector of the ruggedized type was placed at an angle of 120° with respect to the beam axis and collimated by a 0.32 mm wide horizontal slit placed near the beam axis together with a 4 mm O aperture in front of the detector (fig. 2 of ref. 9). Standard signal amplifying and analyzing equipment was used in conjunction with both detectors.
I(Ey =
3. Experimental procedures, data analyses and results 3.1. CHOICE OF CALIBRATION ENERGIES In order to calibrate the beam analyzing magnet over a wide range of field strengths (2.4-12.4 kG), suitable resonance reactions had to be selected according to the following requirements: (i) wellknown resonance energy; (ii) large y-ray yield and, if possible, small total width; (iii) sufficient beam
OF H E A V Y - I O N
175
BEAMS
intensity from the sputtering ion source; (iv) sufficient intensity for the selected charge state of the heavy ion beam with respect to the available high voltage range (0.5-4.0 MV) of the accelerator; (v) availability of the required target nuclei as gases and (vi) distribution of calibration points over the full range of magnetic field strengths in approximately equal steps. These requirements are fairly well fulfilled for the reactions listed in table 1. 3.2. TARGET GASES AND GAS MIXTURES For the measurement of resonance yield curves, the beam intensity in the gas target was monitored by the intensity of the elastically scattered projectiles at 120° backward angle (section 2). Since the total widths of the 13C(p,~')IaN and Z°Ne(p, y)2~Na resonances are rather small (table 1), the elastic scattering yield is, for the target pressures used (table 2), not influenced by interference effects between Coulomb and resonance scattering over the energy region of the resonance. For the broader IaN(p, ~')lsO resonances, however, such effects are expected and therefore the beam intensity was monitored by the elastic scattering yield from Xe nuclei, admixed into the target gas (table 2). The same technique has been applied in the case of the heavy-ion induced reactions on hydrogen target nuclei, since the elastic scattering of heavy-ions from hydrogen target nuclei is only possible in the forward direction. Table 2 summar-
TABLE 1 Resonance reactions, absolute beam energies and charge states of the projectiles and stopping powers of the gas targets. Case Nr. 1 2 3 4 5 6 7 8
Reaction :~
2°Ne(p, 7)2J Na 13C(p, y)14N 2° Ne(p, p'y)2°Ne 14N(p, 7)150 14N(p, y)lsO p(13C, y)14N b p(19F, ~y)16OC p(19F, ~y)16od
Proton-beam e Elab (keV) Fla 0 (keV) 1168.8_+0.8 1747.6_+0.9 1955.0_+2.0 2479.0+ 1.7 4203.0±3.0
Heavy-ion beam f Eub (keV) Fl~b (keV)
(15.5_+1.4)10 -3 (77 ±12)10 -3 3.93±0.10 9.4_+0.5 43±4 22548.2_+11.8 16440.0_+ 5.2 6418.0_+ 1.3
1.0_+0.2 89_+4 45±4
Charge state g
Stopping power h (keV mm I T o r r - 1 )
1 1 1 1 1 5 4 2
0.01998 0.04108 0.01530 0.02244 0.01557 0.5603 1.4111 1.5484
Listed according to increasing magnetic field strengths (B0 =2.4-12.4 kG, table 3). Identical to case nr. 2 in the cm-system. Corresponding2) to Ep (lab) = (872.11 ±0.20)keV [Fla b = (4.7±0.2)keV]. Corresponding 2 ) to Ep (lab) = (340.46 ± 0.04) keV [ Flab = (2.4 ± 0.2)keV]. Refs. 2, 10 and 11. Calculated values from reported proton-induced data 2) using exact masses]°, J3). The errors include the uncertainties in the proton-induced resonance energies and in the relevant masses. g Beam currents of up to 2, 0.3 and 10/IA were used for protons, 13C- and 19F-ions, respectively. h Stopping powers from ref. 12 for the target gas mixtures used (table 2) assume a gas temperature of 20°C. b c d e r
H.P.
176
TRAUTVETTER
et al.
izes the target gases and gas mixtures as well as the total pressures of the gas mixtures employed in the experiments. The H2, N2 and Xe gases were chemically pure to better than one part in 10 -5 . The CO2 gas* was enriched to 90% in ~3C. Although natural neon gas predominantly consists of the isotope 2°Ne (90.5%), the isotope 22Ne (9.2%) produces intense resonances via the 22Ne(p, y)23Na reaction in the same beam energy region. For this reason, enriched 2°Ne gas* (99.95%) was employed in the experiment.
"FABLE
3.3. MEASUREMENT OF RESONANCE YIELD CURVES
a Chemically pure gases ( < 1 0 ppm) with natural isotopic abundances. b Enriched to 90% in 13C. c Enriched to 99.95% in 2°Ne.
The resonance yield curves were deduced from the dominant y-ray transitions in the reaction of interest. Sample y-ray spectra accumulated at the Ecru = 1613 keV resonance of 13C(p, ~')laN and * Monsanto Corporation, Miamisburg, USA.
2
Target gases, gas mixtures and total gas pressures. Reaction
p(13C, y)14 N 13C(p, y)14 N 14N(p, y)t50
2ONe(p ' y)21Na p(19F, aty)16 O
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_
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-
-
3.42 : 1 1.66 : 1
Total pressures (Torr) 1.0, 3.0, 5.0 1.0, 3.0 5.0 1.0, 3.0 0.45
p(13C, )')14N are shown in fig. 2. Theintensity. of the dominant R--,0 (79%) y-ray decay ~l) is normalized to the 120 ° elastic scattering yield of the
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102
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500
1000
1500
2000
1000
tt
I 500
600
CHANNEL
NUMBER Fig. 2. Sample y-ray spectra obtained with the Oe(Li) detector at the Ecm=1613keV resonance of the 13C+p compound nucleus using (a) a proton and (c) a ]3C beam. The high y-ray background observed with the 13C-beam arises predominantly from i2C + 13C reactions of the beam with traces of carbon contaminations on the canals, walls of the target chamber and beam stop (fig. 1). Parts (b) and (d) illustrate the associated particle spectra obtained from the elastic scattering of protons and 13C-ions by the 13CO2 and H 2 + X e gas target mixtures, respectively. These spectra were used to monitor the beam intensity during the runs.
ENERGY DETERMINATION OF HEAVY-ION BEAMS
projectiles. The measurement of the yield curves for both reactions have been carried out at several target gas pressures and the results are illustrated in fig. 3a and b. The yield curve results obtained for the other resonance reactions (table 1) are summarized in fig. 4. After a particular resonance (table 1) had been located, the following precautions were taken prior to the final yield curve measurements: (i) in order to prevent differential hysteresis effects of the analyzing magnet, the magnet was recycled in a procedure similar to that described in ref. 3; (ii) the beam transmission through the gas target system (fig. 1) was optimized at each step in beam energy by maximizing the beam current measured in the Faraday-cup without gas in the target chamber. Nearly full beam transmission was achieved. It should be noted, that reduction of target gas pressure along the beam axis due to space-charge repulsion and hard collisions is not important at the target pressures (up to 5 Tort) and beam currents employed. This feature has been verified experimentally at the E~,b=6418 keV resonance of the p(19F, o:'y)160 reaction using 19F2+ beam currents of 4 and 19~A (fig. 41). 3.4. SHAPE OF THE YIELD CURVES Due to the extended gas target (fig. 1), the location of a given resonance moves along the beam axis as the beam energy is varied. Furthermore, the heavy lead shield around the Ge(Li) y-ray detector defines an effective target length / along the beam axis, where the resonance can be detected (fig. 1). If the target thickness A over this length / is much larger than the resonance width F(A >> 1-3 and if the y-ray detection efficiency is uniform within this effective detection window, the observed y-ray yield curve would be a rectangular step function. The front edge of this function will have, however, a finite slope due to the action of the following effects: (i) the finite resonance width F, (ii) the finite beam energy resolution ~, (iii) the beam energy straggling between the entrance canal A and the beginning of the effective target length /, (iv) the y-ray absorption effects at the edge of the lead collimator and (v) the variation of the solid angle of the detector as seen from the beam axis over the edge of the effective target length. The back edge of this yield curve function should then exhibit the mirror shape of the front edge except that the additional beam en-
177
ergy straggling along the target length / should further decrease the slope of this edge. If the above effects are symmetric in beam energy, the edges of the yield curves should have a shape very similar to the thick-target yield curve of a narrow resonance. Since the efficiency and solid angle of the y-ray detector vary only slightly within the effective target length l, the top of the yield curve is expected to be fiat. This flat top as well as the finite slopes at the front and back edges of the yield curves are indeed observed for target pressures corresponding to the condition A>> F (figs. 3a, 3b and 4a). The observed slopes at the edges of these yield curves originate predominantly from beam energy straggling in the gas target and to a lesser degree by the other effects mentioned above. In the other extreme case, i.e. A <~F, the yield curve should reflect a normal greit-Wigner shape with a width r/ corresponding to the quadratic addition of the resonance width F and the beam energy resolution ~. Intermediate cases can be constructed by folding the Breit-Wigner shape with the profile of the detection efficiency (for a given y-ray energy) in the present set-up (fig. 1). It should be noted that the y-ray yield curves for different gas target pressures have been normalized to the same number of elastically scattered projectiles. Since this number is directly proportional to the gas pressure, the fiat top of the y-ray yield curves should decrease in proportion to the target pressure used if, for all pressures used, the condition A >> F applies. This feature is fairly well fulfilled in the investigations of the E~ab=22548keV resonance of the p(13C, y)laN reaction (fig. 4a and table 1). 3.5. ANALYSIS PROCEDURES
The analysis procedures used in calibrating the magnetic analyzer are illustrated by the example of the E~o = 22 548 keV resonance of p(13C, }')I4N (table 1). The yield curves obtained for target pressures of p = l . 0 , 3.0 and 5.0Torr are shown in fig. 3a. Due to the small total resonance width of Flab = (1.0--+0.2)keV (table 1), the observed widths zl of these yields curves (defined by the midpoints at the front and back edges) are predominantly due to the energy loss of the beam over the effective target length /. The observed width e.g. of A ~ 158 keY for a pressure of 3.0 Torr (fig. 3a) is in excellent agreement with the calculated value of A = 1 6 0 k e V using / = 9 . 5 c m and the stopping
178
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Fig. 3. Resonance 7-ray yield curves For the 13C + p reaction obtained with a 13C (a) and proton (b) beam at different target gas pressures. The central energy shifts as well as the decreasing widths of the curves as a function of target chamber pressure are due to the energy loss of the beam over the distances d and I, respectively (fig. l). The lines through the data points are to guide the eye. The central points of the yield curves for the |3C beam (a) are shown in part (c) as a Function of gas pressure v e r s u s the magnetic field squared.
ENERGY
DETERMINATION
OF H E A V Y - I O N
power value e of table 1 for p = 3.0 Torr. The central point of these yield curves is defined by the half distance between the midpoints of the edges. Since these edges are observed to be nearly symmetrical, this definition insures that the central point is the energy corresponding to the location of the resonance at the center of the target chain•
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ber. This resonance energy is affected by the energy loss ,dE(p) of the beam over the distance d = 10.3 cm from the entrance canal to the center of the target chamber (fig. 1). Since this energy loss ,dE(p) depends directly on the target pressure p, the central points of the yield curves should shift towards lower energy values (or magnetic
ERes=1.169MeV E~ : 3.5LMeV
ERes= 1955 MeV E.~ = 1.63/.MeV
1600
. . . .
179
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Fig. 4. Resonance 7-ray yield curves for p r o t o n - i n d u c e d resonances on 2°Ne (a and b) and 14N (c and d) gas targets. The yield curves for the ]9F-beam on a h y d r o g e n gas target are s h o w n in (e) and (f). The pressures used and the 7-ray energy range analysed are indicated for each reaction. Part (f) d e m o n s t r a t e s that different beam current loads in the gas target do not affect significantly the location o f the central points o f the yield curves. Due to pile-up effects in the y-ray detector at this intense resonance, the 7-ray yield on top o f the resonance is higher at the lower beam currents. The lines through the data points are to guide the eye.
180
H.P.
T R A U T V E T T E R et al.
fields) with decreasing target gas pressure, in accord with observation (fig. 3a). The observed energy of the resonance. ER(P), at the center of the target chamber is therefore related to the true resonance energy E0 (i.e. for an infinite thin target) by the equation ER(P) = E o + A E ( p )
TABLE 3 Results for magnetic field strength and magnet calibration factor. Case nr.
Magnetic field B0 a (G)
Magnet calibration factor K b (G/MeV)
= E o + d~p,
where e is the energy loss in the target gas (table 1). If the central energy E R is plotted as a function of target pressure p, the slope of this straight line is proportional to de and hence the value of e can be determined experimentally. For the H2-Xe gas mixture (tables 1 and 2), the shifts of the yield curve central energies (fig. 3a) result in a stopping power of e=(0.557_+0.014)keV mm 1Torr ~ For a gas temperature of 20°C, the tables of Northcliffe and Schilling 12) lead to a value of e = 0.5603 keV mm I Torr -1 (table 1), in good agreement with the above experimental value. If the magnetic field strength squared B~ (p), corresponding to the central resonance energy E R(p), is plotted versus the target pressure, the extrapolation to " z e r o " pressure ~ leads to the relevant value of B~. For the above resonance, this procedure yields (fig. 3c) a value of B0 = (7692.6_+0.4)G (table 3). In the analyses of the yield curves obtained for all the other resonance reactions, the tables of ref. 12 were used in the determination of the beam energy loss (table 1) over the distance d in the target chamber. The resulting magnetic field strengths B0 are summarized in table 3. The 'following sources of errors were considered for the individual B0-results: a) Statistical error in the central point determination of the yield curves. This error covers also possible asymmetries in the slopes of the front and back edges in the yield curves and is much larger than the uncertainties in the measurement of the absolute magnetic field or in differential hysteresis effects 3) of the analyzing magnet (section 2). b) Due to the rapid pressure reduction (combined with the short distances between the canals) in the gas target system (fig. 1), the energy loss of
Similar procedures in the extrapolation of the front and back edges of the yield curves lead to values of E0 - q/2 and E 0 + q / 2 with r/= v'F2+~ 1. The experiment reveals r/~20 keV, which corresponds to an energy resolution of the 13CS+-beam of ~ < 2 0 k e V .
1 2 3 4 5 6 7 8
2435.9 +_ 0.4 2977.5-+ 1.3 3151.9-+ 0.3 3545.6_+ 2.1 4620.6_+ 1.9 7692.1 _+ 1.3 9914.0+_ 4.2 12373.6_+ 10.9 Weighted average
51.982 -+0.020 51.955_+0.035 51.996-+0.053 51.936_+0.047 51.956+_0.043 52.014+_0.029 51.975-+0.027 51.918+_0.047 51.975 -+0.011 c
a Uncertainties obtained as quadratic addition of the following statistically independent errors: the central point determination of the yield curves, the gas mixing and absolute pressure measurement including effects induced by the beam, the effective length d and the stopping power value ~. b Errors correspond to the quadratic addition of the uncertainties in the magnetic field Bo, the absolute beam energies E0 and the relevant nuclear masses. c Internal error 3) only. The external error 3) is _+0.009.
the beam can be neglected in the gas target system up to the entrance canal A of the target chamber. Assuming that the gas pressure increases linearly within the 1 cm long canal A, the beam equivalently loses energy uniformly from the center of this canal to the center of the target chamber. To this distance of d = 10.3 cm (fig. 1), an error of _+0.7 cm has been assigned to account for the uncertainty of the pressure profile in the canal A (_+0.5 cm) and the position of the Ge(Li) detector within the lead shield (_+0.2 cm). This error is common to all experiments. c) The stopping power values e of ref. 12 were used for a gas temperature of 20°C. The good agreement between the observed and calculated evalues in the case of the p(13C, }')14N experiment (see above) indicates, that temperature effects or changes in gas density along the beam axis in the gas target chamber can be neglected. A 5°C increase in the gas temperature would decrease the e-value by 2% in the above case. Since in this experiment a 13C-beam of only _<50 nA particle current was employed and since such effects are expected to increase with the particle current, the intense t9F beam was used to search for these effects. The results (fig. 4f and section 3.3) reveal that they are negligible ( < 8 % ) for the target pres-
ENERGY
DETERMINATION
sures and particle currents employed. An error in e of _+ 10% has been adopted as a conservative estimate for both these effects and the uncertainties in the tabulated s-values~2). d) Due to an unstable valve in the gas cleaning elements 9) of the gas target system, the gas target pressure could change during the running periods by as much as +0.05 Torr. This uncertainty was common to all experiments. Since all these errors are statistically independent and common to all individual experiments, they have been added quadratically to obtain the total error in the final B0-values (table 3).
OF H E A V Y - I O N
BEAMS
181
w o r k - w i t h a constant calibration factor over the full range of magnetic field strengths, with a weighted average of K = (51.975+0.011) G MeV (table 3). This result implies a precision in the determination of heavy-ion energies of 4 parts in 104 , which is sufficient for all practical purposes of interest (section 1). 3.7. ATOMIC EFFECTS ON NUCLEAR RESONANCE ENERGIES
In the case of nuclear resonance reactions, the nuclear Q-value QN is given by the relation QN = QA + B(Zp) + B(Z,) - B(Z~)
3.6. THE MAGNET CALIBRATION FACTOR
The calibration factor K for the analyzing magnet is defined through the well-known relation 2) K = ZpBo,/\ (2,q%C2Ep +- E~),
where the quantities Zp, mp and Ep a r e the charge state, exact mass and laboratory energy of the projectile, respectively and B0 is the magnetic field of the analyzer. With the values given in tables 1 and 3, the resulting values for the magnet calibration factor K are summarized in table 3 and plotted in fig. 5 as a function of magnetic field strength B0. Since the Z2-fit to the data for a field-independent magnet calibration factor leads to a normalized value of )~2 =0.7, the data are consistent-within the experimental uncertainties of the present
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Fig. 5. Results for the magnet calibration factor K are plotted as a function of magnetic field strength B 0 (table 3). The line through the data points represents the result of a Z2-fit (Z2=0.7) for a field-independent K = ( 5 1 . 9 7 5 _ 0 . 0 1 1 ) G / M e V . The types of projectile ions used in the calibration of the magnetic analyzer are also indicated.
where QA represents the calculated Q-value on the basis of tabulated atomic masses and the quantities B(Zp), B ( Z ) and B(z~) are the total electronic binding energies of the projectile, target and compound atom, respectively. Since the differences in electronic binding energies between the projectile plus target atoms and the compound atom are small, such atomic effects on nuclear resonance energies can usually be neclegted. The existence of such atomic effects on nuclear resonance energies has been demonstrated however, in the high-precision experiment of StaubU). In the elastic scattering of neutral 4He atoms with singly charged 4He+ ions leading to the groundstate of the compound nucleus 8Be, this nuclear resonance has been observed to be splitting up into several nearby resonances, where the energy differences were consistent with the spacing of the lowest few electronic states of the compound atom 8Be. In the present work, for the calibration of the magnetic analyzer at high field strengths, heavyion beams were used to bombard a hydrogen gas target and the energies of these heavy ions were defined by the well-known (proton induced) resonance energies. If in the formation of the compound nucleus the associated compound atom suffers drastic changes, the nuclear resonance energies can again shift or split up by a sizable amount. The effects will be most significant, if, in the formation of the compound nucleus, electrons from the inner shells of the associated electron cloud are excited or removed. For example, if for the E~ab = 6418 keV resonance of the p(19F, 0c7)160 reaction a K-vacancy is created in the formation of the 2°Ne compound atom, the nuclear mass of 2°Ne will increase by 0.869 keV and consequently
182
H . P . TRAUTVETTER et al.
the laboratory resonance energy should increase by A E v -.~ 0.869 x 19 = 16.5 keV. This increase in nuc-
lear resonance energy would correspond to a change in the magnet calibration factor K by A K = 0.065, which is of the same size as the experimental uncertainty (fig. 5 and table 3). For the other heavy-ion induced resonances, the creation of a K-vacancy in the formation of the c o m p o u n d atom would change the magnet calibration factor by AK(19F)= 0.025 and AK(13C)= 0.006, which is again well within the experimental errors (fig. 5 and table 3). Since the details of such atomic effects on the nuclear resonance energies are poorly understood, corrections due to such effects have been omitted in the energy calibration of the magnetic analyzer. It should be pointed out, however, that the experimental uncertainties in the present equipment and set-up (section 3.5) could in principle be reduced significantly, such that the above and other heavy-ion induced resonance reactions on hydrogen gas targets could be used as a tool to study the atomic effects on nuclear resonance energies in more detail. The K.U. course thank ments
authors acknowledge the help of J. G6rres, Kettner and P. Schmalbrock during the of the experiments. We would like to also Dr. W . E . Kieser for the helpful comon the manuscript. The travel supprt prov-
ided by the Westf~ilische Wilhelms-Universit~it Miinster is highly appreciated.
References 1) c. Rolls and H. P. Trautvetter, Experimental nuclear astrophysics, Ann. Rev. Nucl. Sci. 28 (1978) 115. 2) j. B. Marion, Rev. Mod. Phys. 38 (1966) 660; J. B. Marion and F. C. Young, Nuclear reaction analysis (NorthHolland, Amsterdam, 1968). 3) j. C, Overlay, P. D. Parker and D. A. Bromley, Nucl. Instr. and Meth. 68 (1969) 61. 4) M. L. Roush, L. A. West and J. B. Marion, Nucl. Phys. A147 (1970) 235. 5) C. Rolls, W. S. Rodney, S. Durrance and H. Winkler, Nucl. Phys. A240 (1975) 221. 6) T. Freye, H. Lorenz-Wirzba, B. Cleft, H. P. Trautvetter and C. Rolls, Z. Physik A281 (1977) 211. 7) K. Brand, Nucl. Instr. and Meth. 141 (1977) 519. 8) E. Blanke, K. Brand, H. Genz, A. Richter and G. Schrieder, Nucl. Instr. and Meth. 122 (1974) 295. 9) C. Rolls, J. G6rres, K. U. Kettner, H. Lorenz-Wirzba, P. Schmalbrock, H. P. Trautvetter and W. Verhoeven, Nucl. Instr. and Meth. 157 (1978) 19. 10) p. M. Endt and C. van der Leun, Nucl. Phys. A214 (1973) 1. 11) F. Ajzenberg-Selove, Nucl. Phys. A268 (1976) 1. 12) L. C. Northclifte and R. F. Schilling, Nucl. Data Tables 7 (1970) 233. 13) L. G. Smith and A. H. Wapstra, Phys. Rev. Cll (1975) 1392. 14) H. H. Staub, Proc. Int. Conf. At. Masses, ed. R. C. Barber, (University of Manitoba Press, 1967) p. 495; J. Benn, E. B. Dally, H. H. Miiller, R. E. Pixley, H. H. Staub and H. Winkler, Nucl. Phys. A106 (1968) 296.