Absolute Normalizations for 4He Data from 1995 Mainz Run K. A. Aniol, CSULA Introduction and Summary Elastic scattering of the electron beam at 675 MeV and 855 MeV is used to
determine the absolute cross sections for the (e,e'p) data taken on the
4He cryo target at Mainz. Spectrometer B was used to determine the elastic
scattering while spectrometer C, used as a luminosity monitor, was held
fixed at 120 deg scattering angle and a central momentum of 340 MeV/c.
Elastic spectra were taken under different beam currents to establish the
local beam heating effect on count rate. Target empty runs were used to
determine the contributions of the cell walls to the spec C spectrum. Absolute cross sections from previous elastic scattering data were used to
simulate the measurement using the geometry of the cuts from the espace
analysis. From this simulation( using aeexb) it is possible to obtain a
"luminosity factor" for spec C which correctly accounts for the local beam
heating effects expected at higher beam currents.
The luminosity factors derived in this report relate the total number of
counts in the ee'p coincidence measurement, N(rn2,AB,ee'p), for run number
rn2 to the total counts seen in spec C (spectrum no. 16), N(rn2,C,inel),as a monitor with a spectrum cut on variable p18 with the following cuts:
Summary
spectrum no. 16 ( in Spectrometer C)
280<p18<410 MeV/c
cuts thtg18-1 -.07
.07
phtg18-1 -.12 .12
ytg18-1 -.035 .035
ecer16-1 200 2000
angokc thtg18-1.and.phtg18-1
angokc.and.ecer16-1
L(rn2,675 ) = 2.42 e33/cm3 *N(rn2,C,inel) +- 1.2%
L(rn2,855) = 4.32 e33/cm3 *N(rn2,C,inel) +- 2.2%
Contents
1) List of 675 MeV and 855 MeV
elastic data runs and empty cell runs
2) spectrum cuts on specB and net true counts in the elastic peak
4) average
cross sections from gauges and extrapolation to zero current
and comparison of aeexb cross sections with data
5) spectrum cuts in spec C, raw and true counts in C, comparison to elastic counts in B
6) definition of luminosity factors
7) luminosity factors for 675 MeV and 855 MeV data(needs external bremstrahlung)
8) Inclusion
of external bremstrahlung in fits to elastic data-final luminosity factors
1) List of 675 MeV and 855 MeV elastic data and empty cells
675 MeV data
code run number proc. events de.tof
prescale live time I(uA) Q (mC) from logbook
1 950709022047
10
specA
116555 15907.5k
135 0.9892
7.660
specB
117049 1442.5k
12 0.9737
7.650
specC
107204 997.5k
9 0.9673
13.045
___________________________________________________
2 950709024337
30
specA
166036 57497.5k
410 1.18 ?
28.17
specB
171859 5237.5k
35 1.15 ?
28.15
specC
170662 3542.5k
20 0.9635
48.12
____________________________________________________
3 950709030327
1
specA
156815 2177.5k
13 0.9362
1.015
specB
160183 207.5k
1 0.7720
1.015
specC
152576 187.5k
1 0.8137
1.760
______________________________________________________
mt675 950626014409
9
specA
13.255
specB
13.240
specC
176595 1067.5k
6 0.9926
22.715
**********************************************************
855 MeV data
4 950703031817
2
specA
19031 762.5k
40 0.9983
1.365
specB
101456 842.5k
8 0.9634
1.360
specC
55540 167.5k
3 0.9947
2.940
_______________________________________________________
5 950703030615
5
specA
15845
1532.5k 100 1.03 ?
2.840
specB
86236
1752.5k 20 0.9841
2.840
specC
30735
312.5k 10
0.9835
6.150
_________________________________________________________
6 950703025106
10
specA
20771
3632.5k 200 1.14 ?
6.915
specB
105047 4192.5k
40 1.0022
6.920
specC
35481
712.5k 20 0.9960
14.79
___________________________________________________________
mt855 950626044708
specA
43.84
specB
43.825
specC
88967
4727.5k 53
0.9974
95.535
to table of contents
2) Net true counts for elastic scattering
i) spectra generated with a cut on phtg10
These net elastic counts come from the allfit analysis including radiative
corrections and are corrected for dead time and prescaling.
The cuts on the spectra are as follows:
s8 goodzl = (-.03<reactz10<.01)
s9 goodzr = (.01<reactz10<.03)
s10 gdz1&phi1 = (-.01<reactz10<.01)&(-.01<phtg10<.01)
s11 gdz2&phi1 = (-.02<reactz10<.02)&
"
s12 gdz3&phi1 = (-.03<reactz10<.03)&
"
s13 goodzl&phi1
s14 goodzr&phi1
Where phi1 = (-.01<phtg10<.01)
All these cuts also require -.08<ytg10<.08 .
675 MeV Data
1
run_950709022047
spec num Ntrue
+- %
s8
134811 1.5
s9
116150 1.7
s10
61485 2.3
s11
124060 1.6
s12
183315 1.4
s13
61688 2.3
s14
60015 2.3
2
run_950709024337
s8
468189 1.3
s9
421838 1.4
s10
228858 1.9
s11
446350 1.3
s12
469526 1.3
s13
212590 1.9
s14
218585 1.9
3
run_950709030327
s8
16228 1.3
s9
14324 1.5
s10
7464
2.0
s11
14921 1.4
s12
22412 1.2
s13
7574
2.0
s14
7430
2.0
-----------------------------------------------------------
855 MeV data
4
run_950703031817
s8
86157 1.6
s9
76557 1.7
s10
38225 2.4
s11
75846 1.7
s12
112791 1.4
s13
37443 2.4
s14
37194 2.4
5
run_950703030615
s8
170613 1.8
s9
153725 1.9
s10
81122 2.6
s11
158322 1.8
s12
232501 1.5
s13
75811 2.7
s14
74873 2.7
6
run_950703025106
s8
405114 1.6
s9
378100 1.6
s10
192279 2.3
s11
377191 1.6
s12
558919 1.4
s13
178727 2.5
s14
187549 2.4
ii) Spectra generated without a cut on phtg10
all spectra require -8cm<ytg10<8cm, there is no cut on phtg10
spectrum additional cuts
1
none
2 -.01<reactz10<.01
3 -.02<reactz10<.02
4 -.03<reactz10<.03
675 MeV, true net counts in elastic peak
s#
run1
run2
run3
1
48250 (.84%)
1.7288e6(.66%)
65918(.74%)
2
124280(1.63%) 4.501e5(1.33%)
16839(1.43%)
3
251529(1.14%)
8.958e5(.95%)
33648(1.01%)
4
373222(.91%)
1.333e6(.78%)
50589(0.82%)
855 MeV true net counts in elastic peak
s#
run4
run5
run6
1
13.1469e5(.92%) 640269(.97%)
1548056(.83%)
2
82493(1.65%)
172332(1.73%) 407209(1.58%)
3
164985(1.13%)
337957(1.23%) 805039(1.12%)
4
245885(.93%)
498218(1.03%) 1196084(.93%)
3) Gas densities from the gauges.
According to the target log the gauges read the following.
675 MeV elastic
at 00:20 on July 9, I= 0 uA, Ta=20.8K, Tb=20.4K, P=9.5 B
at 09:25 on July 9, I= 0 uA, Ta=20.8K, Tb=20.4K, P=9.0 B
The elastic scattering data were taken between 02:00 and 04:00.
Using the density/pressure/temp table supplied by Dimitri the density
at
00:20 was 0.02211 g/cm3.
855 MeV elastic
at 02:20 on July 3, I=0 uA, Ta=21.4K, Tb=20.5K, P= 5.0B
The elastic data were taken between 02:50 and 04:00.
From Dimitri's tables this corresponds to a density of 0.01147
g/cm3
4) Average cross sections from gauges and extrapolation to zero current
Cross sections are calculated for the spectra of section 2ii)
Q is taken as the logbook Foerster reading for specB
density = 0.02211 g/cm3
espace_1 run_950709022047 I=10 uA 675
MeV, Q=7.650mC
espace_2 run_950709024337 I=30 uA 675
MeV, Q=28.15mC
espace_3 run_950709030327 I=1 uA
675 MeV, Q= 1.015mC(unreliable)
density = 0.01147g/cm3
espace_4 run_950703031817 I=2 uA
855 MeV, Q=13.60mC
espace_5 run_950703030615 I=5 uA
855 MeV, Q= 28.40mC
espace_6 run_950703025106 I=10 uA 855
MeV,Q=6.920mC
Average Elastic Cross Sections = (true counts)/(.0056sR)/Nelec/Ntarg(cm2)
675 MeV data
units cm2/sR * e-32
s# espace_1
espace_2 espace_3
1 6.78(.06)
6.60(.04) 6.98(.05)
2 6.99(.12)
6.87(.09) 7.13(.09)
3 7.07(.10)
6.85(.07) 7.13(.06)
4 7.00(.07)
6.79(.05) 7.14(.05)
avg 7.02(.11) 6.83 (.08)
7.13(.07) , avg based on s2,s3,s4
note - For 1995 the 1 uA current integration has "large" uncertainties.
855 MeV data
units cm2/sr * e-31
s# espace_4
espace_5 espace_6
1 4.79(.05)
4.67(.05) 4.63(.05)
2 5.03(.08)
5.03(.09) 4.88(.08)
3 5.03(.06)
4.93(.06) 4.82(.06)
4 5.00(.05)
4.85(.05) 4.77(.05)
avg 5.02(.07) 4.92(.07)
4.84(.05) , avg based on s2,s3,s4
The values of the cross sections extrapolated to I= 0 uA are,
675Mev sigma elastic = 7.14(.05) e-32 cm2/sr
aeexb simulation gives average cross section = 8.16 e-32 cm2/sr
855 MeV sigma elastic = 5.05(.04) e-31 cm2/sr
aeexb simulation gives average cross section = 5.09 e-31 cm2/sr
The simulation and data agree at 855 MeV to within 1% but the discrepancy
at 675 MeV is data/simulation = 7.14/8.16 = 0.875
5) Spec C counts at 675 and 855 MeV and comparison to elastic counts in Spec B
675 MeV data for spec C and the empty run trying
different cuts to see which gives the most consistent ratios for
spec B elastic and spec C. Note that the counts are for 280<p18<410.
cuts thtg18-1 -.07 .07
phtg18-1 -.12 .12
ytg18-1 -.035 .035
ecer16-1 200 2000
angokc thtg18-1.and.phtg18-1
spectra of variable p18
s# cuts
13 none
14 angokc
15 ecer16-1
16 angokc.and.ecer16-1
17 angokc.and.ecer16-1.and.ytg18-1
For any given spectrum the true counts T for N raw full counts and
B raw empty counts is,
T = (1/live time)*(ps*N) - (Qfull/Qmt)(1/live time_mt)*(ps_mt*B)
T = a(ps*N) - b(ps_mt*B), (dt)^2
= a^2*(ps*N) + b^2*(ps_mt*B)
-----------------------------------------------------------------
Raw Counts in p18 between 280 MeV/c and 410 MeV/c, 675 MeV
s# N#3 N#2
N#1 mt675
13 51187 58190 36645 26122
14 27948 38815 24262 6316
15 8253 12544 7837
433
16 7295 11187 7054
234
17 6666 10282 6523
110
-----------------------------------------------------------
Net True Counts in Spec C , 280<p18<410 with mt subtraction,
675 MeV
s#
T#1+-%
T#2+- %
T#3+- %
13 249931(.25)
872947(.14)
50806(.55)
14 203731(.26)
724723(.14)
31414(.65)
15 71409(.51)
254832(.26)
9939(1.1)
16 64817(.54)
229215(.28)
8854(1.2)
17 60308(.56)
212020(.30)
8138(1.2)
-------------------------------------------------------------
Comparison of spectrum 4 spec B(true elastic counts)from section 2ii)
to spec c
ratio(+- %) 675 MeV
s#
#1(10uA)
#2(30uA)
#3(1uA)
13
1.49(.94)
1.53(.80)
1.0(1.0)
14
1.83(.95)
1.84(.80)
1.61(1.0)
15
5.23(1.0)
5.23(.82)
5.09(1.4)
16
5.76(1.1)
5.82(.83)
5.71(1.4)
17
6.19(1.1)
6.29(.83)
6.22(1.4)
----------------------------------------------------------------------
855 MeV specC data with same cuts as 675 MeV
raw counts for 280<p18<410 MeV/c, 855 MeV
s# 4 5 6 mt855
13
21102
12027
13899
13335
14
13057
8092
9522
3324
15
1488
906
916
105
16
1238
799
916
41
17
1111
708
840
14
----------------------------------------------------------------------------
Net true counts for specC, 855 MeV
s# 4 5 6
13 41654(.61)
76368(.46) 167208(.32)
14
33898(.59) 70831(.41)
163315(.28)
15 4315(1.7)
8850(1.1) 20043(.72)
16 3666(1.8)
7983(1.2)
18050(.8)
17 3328(1.9)
7150(1.3) 16750(.8)
----------------------------------------------------------------------------
ratios of specB elastic s#4 from 2ii) to true specC, 855 MeV, error
in %
s# 4 5 6
13
5.90(1.1)
6.52(1.1)
7.15(1.0)
14
7.25(1.1)
7.03(1.1)
7.32(1.0)
15
56.99(1.9)
56.3(1.5)
59.7(1.2)
16
67.07(2.0)
62.4(1.6) 66.3(1.2)
17
73.9(2.0)
69.7(1.6) 71.4(1.2)
------------------------------------------------------------------------------
6) Definition of "luminosity factors"
We want to relate the counts seen in spec C, the luminosity monitor, to an absolute cross section for the (e,e'p) data. The elastic scattering information is used to make this possible. Consider elastic scattering from the extended target .
J(x,y,t) is the electron current density, assumed independent of z, the beam direction,
r(x,y,t,J) is the gas density in a volume
dxdydz at point (x,y,z). The density depends on the current density. If
s is the differential cross section for scattering
into solid angle dW
then the number of counts dN in a time dt is
dN = (rdxdydz)/(dxdy)*(Jdxdydt)*(sdW).
The solid angle depends on the position along the z axis, but we will ignore the dependence of the solid angle on the transverse coordinates x and y because the wobbled spot is typically 10 to 20 times smaller than the length of the target along z. The total counts N for the course of the measurement is
N =( S r(x,y,t)J(x,y,t)dxdydt ) S dz( S s dW)
We can call the integral over density and electron current L(rn) and the integral of the cross section weighted by dz I(B,el), for the case of run number, rn, where spec B measures elastic scattering, for example. The integral L is the same for both spectrometers C and B and has the units 1/cm3. So for run number rn we can write
N(rn,B,el) = L(rn) I(B,el) and N(rn,C,inel) = L(rn)I(C,inel)
For the case of (e,e'p) the counts N(rn,AB,ee'p) is
N(rn,AB,ee'p) = L(rn) I(AB,ee'p), where
I(AB,ee'p) = S dz ( Ss(We,Wp,Ee) dWedWpdEe ) .
The integral over the elastic scattering in B can be obtained from Marty's aeexb results for the average cross sections, namely
s(aeexb,B,DW,zB)
= I(B,el)/(DW* zB), or I(B,el) =
s(aeexb)*(DW* zB)
.
Where DW = .0056 sr, for example, and zB
= 6 cm, for example.
Then from spec B we can deduce the factor L(rn), L(rn)=N(rn,B,el)/I(B,el).
Knowing L(rn) for the elastic run we then can determine I(C,inel).
I(C,inel) = N(rn,C,inel)/N(rn,B,el) * I(B,el).
Next, suppose we have two runs, rn1 = elastic and rn2 = ee'p then for
these two runs we write,
N(rn2,C,inel)
= L(rn2)*I(C,inel)
N(rn1,C,inel)=L(rn1)*I(C,inel)
and dividing we can solve for L(rn2)
L(rn2) = L(rn1)*(N(rn2,C,inel)/N(rn1,C,inel))
L(rn2) = (N(rn1,B,el)/I(B,el)) * (N(rn2,C,inel)/N(rn1,C,inel))
L(rn2) = (N(rn1,B,el)/s(aeexb)*(DW*zB) )*(N(rn2,C,inel)/N(rn1,C,inel))
and from this factor we can obtain the weighted ee'p cross section integral.
I(AB,ee'p) = Sdz ( Ss(We,Wp,Ee) dWedWpdEe ) = N(rn2,AB,ee'p)/L(rn2)
These last two equations in bold are what we need to get the ee'p cross sections. Once we have chosen a set of elastic data the factor L(rn2) is simply proportional to the number of counts seen by spec C, N(rn2,C,inel).
7) Luminosity factors for 675 and 855 MeV(This
is modified in section 8 for
external bremstrahlung)
From the discussion in 6) we can write the L(rn2) factor as
L(rn2) = { (N(rn1,B,el)/N(rn1,C,inel))/(s(aeexb)*(DW* zB) )}*N(rn2,C,inel)
or
L(rn2) = F(rn1)*N(rn2,C,inel),
F(rn1) = (N(rn1,B,el)/N(rn1,C,inel))/(s(aeexb)*(DW* zB) )
We will take
DW = 0.0056 sr, and zB = 6cm, s(aeexb,675)=
8.168 e-32 cm2/sr ,
s(aeexb,855) = 5.091 e-31 cm2/sr
For the ratios of B elastic to C inelastic we will use s#4 from 2ii) and s#16 from 5).
For 675 MeV this ratio of counts is very stable and the weighted average
is 5.77(1.2%).
For 855 MeV this ratio is more variable, but an uncertainty of 2.2%
would bring all the ratios at the three currents to within 2 error bars
of the weighted average, i.e, 65.3(2.2%).
Putting all this together we conclude that the L(rn2) factors are
at 675 MeV
F(rn2)=5.77(1.2%)/(8.168e-32cm2/sr)/(.0056 sr)/(6cm)
= 2.10 e33/cm3 +- 1.2%
L(rn2,675 ) = 2.10 e33/cm3 *N(rn2,C,inel) +- 1.2%(see
section 8)
at 855 MeV
F(rn2) = 65.3(2.2%)/(5.091e-31cm2/sr)/(.0056 sr)/(6cm)
= 3.82 e33/cm3 +- 2.2%
L(rn2,855) = 3.82 e33/cm3 *N(rn2,C,inel) +- 2.2%(see section 8)
8) Inclusion of External Bremstrahlung in fits to the Elastic Spectra
The effect of the inclusion of the walls of the target cell as sources of external bremstrahlung is to increase the deduced number of true counts in the elastic spectra. This is done in allfit by changing the histogram file header information to include a second isotope(iron) along the lines suggested by Richard Florizone in his thesis. This means that the iron seen by the beam is imagined to be uniformly distributed throughout the target gas. The cross section for helium elastic scattering scales as 1/density for the range investigated (9 to 13 mg/cm3 at 855 MeV and 20 to 24 mg/cm3 at 675 MeV). This means that the number of counts deduced by allfit to be in the elastic peak can simply be extracted from a given fitting run with a given density. The densities I chose to fit were 11.85 mg/cm3 at 855 MeV and 22.11 mg/cm3 at 675 MeV.
855MeV
isotope2 = Fe, at 165um and 7.86g/cm3
-> d2 = 129.69 mg/cm2,A2 = 55.847, z2 = 26
isotope1 = 4He, 8cm and 11.85 mg/cm3
-> d1= 94.8 mg/cm2
atomic fraction 4He = 0.911
atomic fraction Fe = .089
effective density = (94.8 + 129.69)/8
mg/cm3 = 28.06 mg/cm3
for run#6, spectrum 8 (+- 3cm on ztg10), N(Fe,allfit) = 32007
675 MeV
isotope2 same as for 855 MeV
isotope1 4He, 8cm and 22.11 mg/cm3->
d1 = 176.88 mg/cm2
atomic fraction 4He = 0.9501
atomic fraction Fe = 0.04989
effective density = (176.88 + 129.69)/8
= 38.32 mg/cm3
for run#1, spectrum 4(+- 3cm on ztg10), N(Fe,allfit) = 32695
True counts in the elastic peak
Using the prescale and dead time information the true counts in the elastic peak are
675 MeV
855 MeV
run 1, spectrum 4
run 6, spectrum 8
with iron
402805
1277399
previous
fit without Fe
373222
1196084
Fe/(no Fe)
1.079
1.068
Cross Sections using the gauge densities
The solid angle assumed is for
-.062< thtg10<.07, DW
= 0.00528 sr.
Target length = 6cm
675 MeV
855 MeV
density
22.11 mg/cm3
11.47 mg/cm3
charge(mC)
7.650
6.920
s(10uA)
8.00 e-32 cm2/sr
4.93 e-31 cm2/sr
s(0uA)
8.16(.06)e-32 cm2/sr 5.21(.05) e-31 cm2/sr
s(aeexb)
8.16 e-32 cm2/sr
5.091 e-31 cm2/sr
Luminosity Factors
Luminosity factors are calculated as in 7) except the true elastic counts are those with the Fe external bremstrahlung included and the solid angle for B is assumed to be .00528 sr.
True counts in spectrum #4 for all runs and the monitor(s#16)
run#
Ntrue(B_s4)
Ntrue(C_s16)
Ntrue(B)/Ntrue(C)
675 MeV
1
402805(.93%) 64187(.54%)
6.21(1.06%)
2
1439845(.82%) 229215(.28%)
6.28(.87%)
3
55472(.82%)
8854(1.2%)
6.27(1.45%)
weighted average
6.25(1.24%)
855 MeV
4
263243(.93%) 3666(1.8%)
71.81(2.03%)
5
531876(1.03%) 7983(1.2%)
66.63(1.58%)
6
1277399(.93%) 18050(.8%)
70.77(1.23%)
weighted average
69.68(2.2%)
F(rn1,675MeV) = 6.25(1.2%)/(8.168e-32)/(.00528)/6 = 2.415e33
F(rn1,855MeV) = 69.68(2.2%)/(5.091e-31)/(.00528)/6 = 4.322e33
L(rn2,675 MeV) = 2.415(+- 1.2%) e33/cm3 * N(rn2,C,inel)
L(rn2,855 MeV) = 4.322(+- 2.2%) e33/cm3 * N(rn2,C,inel)