Integrated yields - Revision history

Hayes: separated p-gamma event calculation into a new subsection

2011-06-15T13:40:09Z

separated p-gamma event calculation into a new subsection

← Older revision		Revision as of 13:40, 15 June 2011
Line 14:		Line 14:

	After an integration, the cross section in mb is obtained by multiplying the yield by		After an integration, the cross section in mb is obtained by multiplying the yield by
-	the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>. ~~You can also calculate the absolute~~	+	the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>.
-	~~p-gamma counts expected using the equation following equation 6.44b in the manual:~~	+

-	Detected p-gamma coincident events	+	===Detected p-gamma coincident events===
		+
		+	The absolute p-gamma counts expected can be calculated using the equation following equation 6.44b in the manual:

	<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>, (1)		<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>, (1)
Line 23:		Line 24:
	where <math>Q</math> is the integrated beam current incident on the target during the experiment, <math>q</math> is the average charge state of the beam, <math>e</math> is the electron charge,		where <math>Q</math> is the integrated beam current incident on the target during the experiment, <math>q</math> is the average charge state of the beam, <math>e</math> is the electron charge,

-	If the absolute efficiency is known well, then it is possible to ~~retrieve~~	+	If the absolute efficiency is known well, then it is possible to reproduce
	the actual counts measured in the photopeak by putting the efficiency into this		the actual counts measured in the photopeak by putting the efficiency into this
	equation.		equation.

128.151.144.176: added link to new 4pi array page

2011-06-02T12:24:24Z

added link to new 4pi array page

← Older revision		Revision as of 12:24, 2 June 2011
Line 40:		Line 40:

	Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.		Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.
		+
		+	==Representing a <math>4\pi</math> Array in Gosia==
		+
		+	A <math>4\pi</math> array can be represented in Gosia in a single calculation without summing the output of a large number of detectors. See the page on [[four_pi_arrays \| 4pi arrays]].

128.151.144.176: moved 4pi array representation to a new page

2011-06-02T12:22:26Z

moved 4pi array representation to a new page

← Older revision		Revision as of 12:22, 2 June 2011
Line 40:		Line 40:

	Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.		Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.
-
-
-
-	~~==Quickly representing a summed 4pi array==~~
-
-	Gosia can quickly integrate the p-<math>\gamma</math> events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position. In order to do this, the output file 9 can be modified to make the first two attenuation coefficients 0 for all orders. (File 9 is the output of OP,GDET, commonly called the .gdt file. For Gammasphere the .gdt file would look something like
-
-	~~<pre>~~
-	1
-	~~25.0~~
-	~~5.000E-02~~
-	~~0. 0. 0.9951~~
-	~~0. 0. 0.9854~~
-	~~0. 0. 0.9711~~
-	~~0. 0. 0.9521~~
-	~~0. 0. 0.9379~~
-	~~0. 0. 0.9013~~
-	~~0. 0. 0.8699~~
-	~~0. 0. 0.8349~~
-	~~</pre>~~
-
-	~~where the first two columns have been set to 0. to simulate a 4pi array. In this case the <math>\epsilon_\gamma</math> value would~~
-	~~still be the absolute photopeak efficiency, but <math>\Delta\Omega_\gamma</math> would be 4*pi.~~
-
-	~~See the manual entries on OP,GDET and "Gamma Detector Solid Angle Attenuation Factors" for more information on these attenuation coefficients.~~

128.151.144.176: still in progress

2011-06-01T19:42:48Z

still in progress

← Older revision		Revision as of 19:42, 1 June 2011
Line 19:		Line 19:
	Detected p-gamma coincident events		Detected p-gamma coincident events

-	<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>	+	<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>, (1)
		+
		+	where <math>Q</math> is the integrated beam current incident on the target during the experiment, <math>q</math> is the average charge state of the beam, <math>e</math> is the electron charge,

	If the absolute efficiency is known well, then it is possible to retrieve		If the absolute efficiency is known well, then it is possible to retrieve
Line 31:		Line 33:
	<math>\epsilon_\gamma</math> is 0.1 to 0.15. If the solid angle subtended by the crystal is ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01</math>.		<math>\epsilon_\gamma</math> is 0.1 to 0.15. If the solid angle subtended by the crystal is ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01</math>.

-	If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be ~~obtained:~~	+	If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be reproduced. By appropriately combining the terms in equation (1) above, it can be rewritten
		+
		+	<math> N_\gamma = 10^{-30} N_p [N_A / A] Y_\gamma \epsilon_p \epsilon_\gamma \Delta\Omega_\gamma </math> (2),

-	<~~pre~~>	+	where <math>N_p</math> is the total number of ''incident'' particles, <math>N_A</math> is Avogadro's number, <math>A</math> is the mass number of the target species, <math>Y_\gamma</math> the yield given by Gosia (using OP,INTI), <math>\epsilon_p</math> is the particle-detection efficiency, <math>\epsilon_\gamma</math> is the <math>\gamma</math>-detector absolute photopeak efficiency, and <math>\Delta\Omega_\gamma</math> is the solid angle subtended by the Ge detector.
-	~~N...~~	+
-	</~~pre~~>	+

	Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.		Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.
Line 43:		Line 45:
	==Quickly representing a summed 4pi array==		==Quickly representing a summed 4pi array==

-	Gosia can quickly integrate the p-gamma events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position. In order to do this, the output file 9 can be modified to make the first two attenuation coefficients 0 for all orders. (File 9 is the output of OP,GDET, commonly called the .gdt file. For Gammasphere the .gdt file would look something like	+	Gosia can quickly integrate the p-<math>\gamma</math> events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position. In order to do this, the output file 9 can be modified to make the first two attenuation coefficients 0 for all orders. (File 9 is the output of OP,GDET, commonly called the .gdt file. For Gammasphere the .gdt file would look something like

	<pre>		<pre>

Hayes: more clean-up

2011-06-01T14:24:05Z

more clean-up

← Older revision		Revision as of 14:24, 1 June 2011
Line 19:		Line 19:
	Detected p-gamma coincident events		Detected p-gamma coincident events

-	<math>N_i = 10^(-30) [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>	+	<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>

	If the absolute efficiency is known well, then it is possible to retrieve		If the absolute efficiency is known well, then it is possible to retrieve
Line 34:		Line 34:

	<pre>		<pre>
-	N	+	N...
-	<\pre>	+	</pre>

-	Refer to the page on the [particle_singles], which is a cross section given in the same output with the integrated yields.	+	Refer to the page on the [[particle_singles \| particle singles]], which is a cross section given in the same output with the integrated yields.



-	~~Maybe~~ the ~~answer to your last question is obvious now, but..~~. ~~I would not try~~	+	==Quickly representing a summed 4pi array==
-	to ~~think of~~ this ~~as correcting for 4pi~~, ~~since~~ the ~~gamma-ray angular~~	+
-	~~distribution has to~~ be ~~calculated as a function of theta, phi for 4pi in order~~	+	Gosia can quickly integrate the p-gamma events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position. In order to do this, the output file 9 can be modified to make the first two attenuation coefficients 0 for all orders. (File 9 is the output of OP,GDET, commonly called the .gdt file. For Gammasphere the .gdt file would look something like
-	to make ~~that correction~~. ~~If you really want Gosia to tell you what~~ the ~~total~~	+
-	~~yield would be for a 4pi array~~, ~~you can change~~ the *.gdt file ~~entries after~~	+
-	~~running OP,GDET~~. For Gammasphere the *.gdt file would look something like	+

	<pre>		<pre>
Line 62:		Line 59:
	</pre>		</pre>

-	where the first two columns have been set to 0. to simulate a 4pi array~~--no~~	+	where the first two columns have been set to 0. to simulate a 4pi array. In this case the <math>\epsilon_\gamma</math> value would
-	~~angular attenuation. Then you would have in the YIELD column of the output the~~	+	still be the absolute photopeak efficiency, but <math>\Delta\Omega_\gamma</math> would be 4*pi.
-	~~p-gamma events where the particle hit the detector as you defined it and the~~	+
-	~~gamma ray is measured at all angles~~. In this case the ~~epsilon_gamma~~ would	+
-	still be the absolute photopeak efficiency, but ~~DeltaOmega_gamma~~ would be 4*pi.	+
-		+
-	~~See pages 48 and 117 in the newest manual version, if you want to do this. You~~	+
-	~~should be able to figure out that the first two entries in the file above~~	+
-	~~should be zero to represent a perfect 4pi array~~.	+

-	~~I hope that is all clear. I can't ever figure out a brief way to explain~~	+	See the manual entries on OP,GDET and "Gamma Detector Solid Angle Attenuation Factors" for more information on these attenuation coefficients.
-	~~things. Maybe after you figure this out~~, ~~you can put it~~ on ~~the Wiki. Your~~	+
-	~~questions come up often~~.	+

Hayes: partial clean-up

2011-06-01T14:06:25Z

partial clean-up

← Older revision		Revision as of 14:06, 1 June 2011
Line 17:		Line 17:
	p-gamma counts expected using the equation following equation 6.44b in the manual:		p-gamma counts expected using the equation following equation 6.44b in the manual:

-	Detected p-gamma coincident events <math>N_i = 10^(-30) [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>	+	Detected p-gamma coincident events
		+
		+	<math>N_i = 10^(-30) [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>

	If the absolute efficiency is known well, then it is possible to retrieve		If the absolute efficiency is known well, then it is possible to retrieve
Line 23:		Line 25:
	equation.		equation.

-	In the equation above the <math>~~epsilon_gamma~~</math> is the absolute	+	In the equation above the <math>\epsilon_\gamma</math> is the absolute
	efficiency as a fraction between 0 and 1 (not including angular effects already		efficiency as a fraction between 0 and 1 (not including angular effects already
	integrated in the "yield"). Let this be called the absolute photopeak efficiency.		integrated in the "yield"). Let this be called the absolute photopeak efficiency.
-	The <math>\Delta\~~Omega_gamma~~</math> term is the solid angle of the Ge detector. A typical absolute photopeak efficiency <math>\epsilon_\gamma<\math> is ~~10--~~15%. If the solid angle subtended by the crystal is ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01<\math>.	+	The <math>\Delta\Omega_\gamma</math> term is the solid angle of the Ge detector. A typical absolute photopeak efficiency
		+	<math>\epsilon_\gamma</math> is 0.1 to 0.15. If the solid angle subtended by the crystal is ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01</math>.

	If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be obtained:		If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be obtained:

Hayes at 14:02, 1 June 2011

2011-06-01T14:02:51Z

← Older revision		Revision as of 14:02, 1 June 2011
Line 2:		Line 2:

	Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG)		Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG)
-	including all feeding, internal conversion branches and angular distributions.	+	including all feeding, internal conversion branches and angular distributions. These calculations are referred to as ''integrations'' below.
	The p-<math>\gamma</math> angular distribution is integrated over the target thickness and		The p-<math>\gamma</math> angular distribution is integrated over the target thickness and
-	the Ge solid angles, but the resulting "YIELD" is quoted in units of <math>mb (mg/cm^2) / sr</math>.	+	the Ge solid angles, but the resulting "YIELD" is quoted in units of <math>mb (mg/cm^2) / sr</math>, where sr represents the solid
		+	angle subtended by the Ge. This leads to some common misunderstandings.

-	~~This leads to a common misunderstanding~~-~~-that Gosia~~	+	The quoted yields represent the absolute cross sections for the chosen particle scattered into the solid angle of the particle detector and the <math>\gamma</math>-ray emitted into the solid angle of the Ge crystal or array, whichever is defined by the user.
-	~~does almost everything~~. The reason for the confusion is in the units and two	+
-	factors--the target thickness and the Ge solid angle--that must be applied	+	The reason for the confusion is usually the units of the YIELD output and two
		+	factors—the target thickness and the Ge solid angle—that often must be applied
	after the integration.		after the integration.

-	~~The "yield" from gosia is in mb(mg/cm^2)/sr, where sr represents the solid~~	+	After an integration, the cross section in mb is obtained by multiplying the yield by
-	~~angle of the Ge. In the case of a raw detector, it should be the total solid~~	+	the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>. You can also calculate the absolute
-	~~angle of all crystals in the raw cluster. So, after~~ an ~~OP,INTG or OP,INTI~~	+	p-gamma counts expected using the equation following equation 6.44b in the manual:
-	~~calculation~~, the cross section in mb is obtained by multiplying the yield by	+
-	the Ge solid angle in sr and dividing by the target thickness in mg/cm^2. You can also ~~check~~ the absolute	+
-	p-gamma counts expected using equation ~~after~~ 6.44b in the ~~most recent~~ manual ~~version~~:	+

-	Detected p-gamma coincident events Ni = 10^(-30)[Q/qe][N_A/A] Y(I-->I_f) epsilon_p ~~epsilon_gamma~~	+	Detected p-gamma coincident events <math>N_i = 10^(-30) [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>
-	~~DeltaOmega_gamma~~	+

-	If ~~your~~ absolute efficiency is known well, then ~~you should be able~~ to retrieve	+	If the absolute efficiency is known well, then it is possible to retrieve
-	the actual counts in the ~~peak, since you are~~ putting the efficiency into ~~the~~	+	the actual counts measured in the photopeak by putting the efficiency into this
	equation.		equation.

-	In the equation above ~~and your equation (1),~~ the epsilon_gamma is the absolute	+	In the equation above the <math>epsilon_gamma</math> is the absolute
	efficiency as a fraction between 0 and 1 (not including angular effects already		efficiency as a fraction between 0 and 1 (not including angular effects already
-	integrated in the "yield"). ~~I think~~ this ~~is properly~~ called ~~the intrinsic~~	+	integrated in the "yield"). Let this be called the absolute photopeak efficiency.
-	~~efficiency, but I always worry that people understand the terms differently. I~~	+	The <math>\Delta\Omega_gamma</math> term is the solid angle of the Ge detector. A typical absolute photopeak efficiency <math>\epsilon_\gamma<\math> is 10--15%. If the solid angle subtended by the crystal is ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01<\math>.
-	~~would call it~~ the absolute photopeak efficiency~~, not efficiency per unit solid~~	+
-	~~angle, because the solid angle is in the yield~~ term ~~and Delta_Omega. The~~	+
-	~~DeltaOmega_gamma~~ is the solid angle of the ~~crystal or cluster~~. ~~I would expect~~	+
-	~~your~~ efficiency ~~epsilon_gamma to be~~ 10--15%. If ~~you have about 0.1 sr~~ solid	+
-	angle subtended by a crystal, then for one crystal epsilon_gamma *	+
-	~~DeltaOmega_gamma~~ ~ 0.01~~, and for a cluster of 4 ~0.04.~~	+
-		+
-	~~So you can see if the numbers match what you fit in the energy spectrum~~.	+

-	~~The answer to your first question, is~~ the ~~factor N_gamma_p only~~ the ~~sum below~~	+	If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be obtained:
-	the ~~photo-peak~~, ~~is yes, as long as you are using~~ the ~~photopeak efficiency as I~~	+
-	~~mentioned above.~~	+

-	~~You definitely don't need any other corrections for the cascade in Gosia's~~	+	<pre>
-	~~"yield."~~	+	N
		+	<\pre>

-	~~About~~ the ~~"singles," they are~~ the ~~latter: the total number of particles hitting~~	+	Refer to the page on the [particle_singles], which is a cross section given in the same output with the integrated yields.
-	~~the detector. Gosia should reproduce this number using the "integrated~~	+
-	~~rutherford cross section~~," which ~~probably shouldn't be called "Rutherford,"~~	+
-	~~because it includes all the inelastic events. For the scattering kinematics,~~	+
-	~~Gosia assumes that the Q-value~~ is ~~the energy of the first excited state--state~~	+
-	#2 in ~~LEVE. You can change this using~~ the ~~CONT option NCM, if you think that~~	+
-	the ~~probability of that state is <<1, for example. In that case, you might~~	+
-	~~pick the ground state~~. ~~If you put~~	+

-	~~OP,STAR~~
-	~~OP,EXIT~~

-	~~in place of OP,YIEL, you can quickly see the probabilities of all states in the~~
-	~~excitation.~~

	Maybe the answer to your last question is obvious now, but... I would not try		Maybe the answer to your last question is obvious now, but... I would not try

128.151.144.176: creation--rough draft from an email

2011-06-01T13:37:37Z

creation--rough draft from an email

New page

==The meaning of Gosia's YIELD output==

Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG)
including all feeding, internal conversion branches and angular distributions.
The p-<math>\gamma</math> angular distribution is integrated over the target thickness and
the Ge solid angles, but the resulting "YIELD" is quoted in units of <math>mb (mg/cm^2) / sr</math>.

This leads to a common misunderstanding--that Gosia
does almost everything. The reason for the confusion is in the units and two
factors--the target thickness and the Ge solid angle--that must be applied
after the integration.

The "yield" from gosia is in mb(mg/cm^2)/sr, where sr represents the solid
angle of the Ge. In the case of a raw detector, it should be the total solid
angle of all crystals in the raw cluster. So, after an OP,INTG or OP,INTI
calculation, the cross section in mb is obtained by multiplying the yield by
the Ge solid angle in sr and dividing by the target thickness in mg/cm^2. You can also check the absolute
p-gamma counts expected using equation after 6.44b in the most recent manual version:

Detected p-gamma coincident events Ni = 10^(-30)[Q/qe][N_A/A] Y(I-->I_f) epsilon_p epsilon_gamma
DeltaOmega_gamma

If your absolute efficiency is known well, then you should be able to retrieve
the actual counts in the peak, since you are putting the efficiency into the
equation.

In the equation above and your equation (1), the epsilon_gamma is the absolute
efficiency as a fraction between 0 and 1 (not including angular effects already
integrated in the "yield"). I think this is properly called the intrinsic
efficiency, but I always worry that people understand the terms differently. I
would call it the absolute photopeak efficiency, not efficiency per unit solid
angle, because the solid angle is in the yield term and Delta_Omega. The
DeltaOmega_gamma is the solid angle of the crystal or cluster. I would expect
your efficiency epsilon_gamma to be 10--15%. If you have about 0.1 sr solid
angle subtended by a crystal, then for one crystal epsilon_gamma *
DeltaOmega_gamma ~ 0.01, and for a cluster of 4 ~0.04.

So you can see if the numbers match what you fit in the energy spectrum.

The answer to your first question, is the factor N_gamma_p only the sum below
the photo-peak, is yes, as long as you are using the photopeak efficiency as I
mentioned above.

You definitely don't need any other corrections for the cascade in Gosia's
"yield."

About the "singles," they are the latter: the total number of particles hitting
the detector. Gosia should reproduce this number using the "integrated
rutherford cross section," which probably shouldn't be called "Rutherford,"
because it includes all the inelastic events. For the scattering kinematics,
Gosia assumes that the Q-value is the energy of the first excited state--state
#2 in LEVE. You can change this using the CONT option NCM, if you think that
the probability of that state is <<1, for example. In that case, you might
pick the ground state. If you put

OP,STAR
OP,EXIT

in place of OP,YIEL, you can quickly see the probabilities of all states in the
excitation.

Maybe the answer to your last question is obvious now, but... I would not try
to think of this as correcting for 4pi, since the gamma-ray angular
distribution has to be calculated as a function of theta, phi for 4pi in order
to make that correction. If you really want Gosia to tell you what the total
yield would be for a 4pi array, you can change the *.gdt file entries after
running OP,GDET. For Gammasphere the *.gdt file would look something like

<pre>
1
25.0
5.000E-02
0. 0. 0.9951
0. 0. 0.9854
0. 0. 0.9711
0. 0. 0.9521
0. 0. 0.9379
0. 0. 0.9013
0. 0. 0.8699
0. 0. 0.8349
</pre>

where the first two columns have been set to 0. to simulate a 4pi array--no
angular attenuation. Then you would have in the YIELD column of the output the
p-gamma events where the particle hit the detector as you defined it and the
gamma ray is measured at all angles. In this case the epsilon_gamma would
still be the absolute photopeak efficiency, but DeltaOmega_gamma would be 4*pi.

See pages 48 and 117 in the newest manual version, if you want to do this. You
should be able to figure out that the first two entries in the file above
should be zero to represent a perfect 4pi array.

I hope that is all clear. I can't ever figure out a brief way to explain
things. Maybe after you figure this out, you can put it on the Wiki. Your
questions come up often.