TF SPIM StoppingPower - Revision history

Foretony: /* (Vavilou's Theory) */

2025-02-26T17:51:37Z

(Vavilou's Theory)

2025-02-26T17:48:17Z

(Landau Theory)

2025-02-26T17:45:37Z

(Vavilou's Theory)

2025-02-26T17:44:48Z

(Vavilou's Theory)

2025-02-26T05:42:49Z

Delta-electrons

2025-02-26T05:42:30Z

Delta-electrons

2025-02-26T05:37:54Z

Fluctuations Model: kappa < 10

2016-09-23T14:46:53Z

Thick Absorber

2015-09-23T16:53:35Z

Multiple Scattering

2015-09-23T16:39:24Z

Delta-electrons

@@ Line 339: / Line 339: @@
 : <math>S_i(y) \equiv \int_0^{y} \frac{\sin(t)}{t} dt</math>
 : <math>C = 0.577</math>
-:<math>C_i</math> and <math>S_i</math> are the sine and cosine integral functions given in Vavilous' paper
+:<math>\lambda_1 = \int_{\Delta}^{\infty} P(x,\Delta) d \Delta </math> are the sine and cosine integral functions given in Vavilous' paper
 [[Image:SPIM_Vavilou_Landau_ThinAbsorber.jpg | 400 px]]

@@ Line 310: / Line 310: @@
 where
-: <math>\lambda = \frac{1}{\bar{\Delta}} \left [ \Delta - \bar{\Delta} \ln \bar{\Delta} - \ln \epsilon + 1 -C \right ]</math>
+: <math>\lambda = \frac{1}{\bar{\Delta}} \left [ \Delta - \bar{\Delta} \ln \bar{\Delta} - \ln \epsilon + 1 -C \right ]</math> Landau's parameter
 : <math>\bar{\Delta} = 2\pi N_a r_e^2 m_e c^2 \rho \frac{Zz^2}{A \beta^2}x</math>
 :<math>\ln \epsilon = \ln \left [ \frac{(1-\beta^2)I^2}{2m_ec^2 \beta^2} \right ]</math>

@@ Line 339: / Line 339: @@
 : <math>S_i(y) \equiv \int_0^{y} \frac{\sin(t)}{t} dt</math>
 : <math>C = 0.577</math>
-:<math>C_i and S_i</math> are the sine and cosine integral functions given in Vavilous' paper
+:<math>C_i</math> and <math>S_i</math> are the sine and cosine integral functions given in Vavilous' paper
 [[Image:SPIM_Vavilou_Landau_ThinAbsorber.jpg | 400 px]]

@@ Line 339: / Line 339: @@
 : <math>S_i(y) \equiv \int_0^{y} \frac{\sin(t)}{t} dt</math>
 : <math>C = 0.577</math>
 [[Image:SPIM_Vavilou_Landau_ThinAbsorber.jpg | 400 px]]

@@ Line 367: / Line 367: @@
 What is a <math>\delta</math> - electron?
-<math>\delta</math> - electrons are also known as "knock -on" electrons and delta rays.
+<math>\delta</math> - electrons are also known as "knock -on" electrons or delta rays.
 As heavy particles traverse a medium they can ionize electrons from atoms.  The ejected electrons (<math>\delta</math> - electrons) can be given enough energy to ionize as well.

@@ Line 369: / Line 369: @@
 <math>\delta</math> - electrons are also known as "knock -on" electrons and delta rays.
-As heavy particles traverse a medium they can ionize electrons from atoms.  The ejected electrons can be given enough energy to ionize as well.
+As heavy particles traverse a medium they can ionize electrons from atoms.  The ejected electrons (<math>\delta</math> - electrons) can be given enough energy to ionize as well.
 In a cloud chamber (a supercooled volume of super saturated water vapor which ionizes as charged particles pass through)  such and event would look like:

@@ Line 393: / Line 393: @@
 ; Fluctuations Model
-:# the atom is assumed to have on 2 energy levels <math>E_1</math> and <math>E_2</math>
+:# the atom is assumed to have 2 energy levels <math>E_1</math> and <math>E_2</math>
 :# you can excite the atom and lose either <math>E_1</math> or <math>E_2</math> or you can ionize the atom and lose energy according to a <math>\frac{1}{E^2}</math> function <math>u_j</math>.

@@ Line 217: / Line 217: @@
 ==== Thick Absorber ====
-A thick absorber is one in which a large number of collisions takes place.   In this situation the central limit theorem from statistics tells you that the larger number of random variables <math>N</math> involved will result in observables which are distributed in a Gaussian manner. The Gaussian distribution is a good approximation to the binomial distribution when the number of trials is large.
+A thick absorber is one in which a large number of collisions takes place.   In this situation the central limit theorem from statistics tells you that the larger the number of random variable samples , <math>N</math>, involved the more the observable will follow a Gaussian distribution. The Gaussian distribution is a good approximation to the binomial distribution when the number of trials is large.
 [[Forest_ErrAna_StatDist#Binomial_with_Large_N_becomes_Gaussian]]

@@ Line 576: / Line 576: @@
 : For thin materials.
 : If the probability of more than 1 coulomb scattering is small
-:The use the Rutherford formula for <math>\frac{d \sigma}{d \Omega}</math>
+:Then use the Rutherford formula for <math>\frac{d \sigma}{d \Omega}</math>
 ;2.)Multiple Scattering:

@@ Line 375: / Line 375: @@
 [[Image:SPIM_DeltaRay_CloudChamber.jpg | 400 px]]
-The blue spiral in the above gas chamber picture is a high energy electron ejected from a collision that spirals in the B-field at near the end of its trajectory ejects low energy electrons.  The B-field is directed out of the picture.
+The blue spiral in the above gas chamber picture is a high energy electron ejected from a collision that spirals in the B-field ejecting low energy electrons at the end.  The B-field is directed out of the picture.
 The physics of ionization is different from the physics used to calculate Bethe-Bloch energy loss.  Remember Bethe-Bloch  starts to break down at low energies below the Bragg peak.