Refactorable number - Revision history

140.115.137.117 at 03:17, 28 October 2014

2014-10-28T03:17:15Z

← Older revision		Revision as of 05:17, 28 October 2014
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	~~In [[particle physics]], the '''threshold energy''' for production of a particle~~ is the ~~minimum [[kinetic energy]] a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal~~ to ~~the rest energy of the desired particle. In most cases, since momentum is also conserved, the threshold energy is significantly greater than the rest energy of the desired particle -~~ and ~~thus there will still be considerable kinetic energy in the final particles~~.		Alyson is the name people use to call me and I think it seems quite great when you say it. What me and my family adore is bungee leaping but I've been using on new things lately. I've always loved living in Mississippi. Credit authorising is where my primary income comes from.<br><br>Here is my site best psychics ([http://cspl.postech.ac.kr/zboard/Membersonly/144571 Check Out cspl.postech.ac.kr])

	~~==Example==~~
	~~Look at the reaction of a proton hitting a stationary proton, <math> p + p \to p + p + \pi^0</math>.~~

	~~By going into the center of mass frame,~~ and ~~assuming the outgoing particles have no kinetic energy the conservation of energy equation~~ is:

	~~<math> E = 2\gamma m_pc^2 = 2 m_pc^2+ m_\pi c^2</math>~~

	~~<math> \gamma = \frac{1}{\sqrt{1-\beta^2}} = \frac{2 m_pc^2+ m_\pi c^2}{2 m_pc^2} </math>~~

	~~<math> \beta^2 = 1-(\frac{2 m_pc^2}{2 m_pc^2+ m_\pi c^2})^2 \approx 0.13 </math>~~

	~~Using relativistic velocity additions:~~

	~~<math> v_\text{lab} = \frac{u_\text{cm} + v_\text{cm}}{1+u_\text{cm}v_\text{cm}/c^2} \approx 0.64 c</math>~~

	~~So the energy of the proton must be <math> E = \gamma m_p c^2 = \frac{m_p c^2}{\sqrt{1-\beta^2}} = 1221\,</math>MeV~~.

	~~== A more general example ==~~

	~~Let~~'~~s look at the case where a particle 1 with lab energy <math>E_1</math> (momentum <math>p_1</math>)~~
	~~and mass <math>m_1</math> impinges on a~~
	~~target particle 2 at rest~~ in ~~the lab, i~~.~~e. with lab energy and mass <math>E_2 = m_2</math>.~~
	~~The threshold energy <math>E_{1,\text{thr}}</math> to produce three particles of masses <math>m_a</math>, <math>m_b</math>,~~
	~~<math>m_c</math>, i~~.e.

	<~~math~~> ~~1 + 2 \to a + b + c,~~<~~/math>~~

	~~is then found by asking these three particles to be at rest in the center of mass frame (symbols with~~
	~~hat indicate quantities in the center of mass frame):~~

	~~<math> E_\text{cm} = m_a c^2+ m_b c^2 + m_c c^2 = \hat{E}_1 + \hat{E}_2 = \gamma (E_1 - \beta p_1 c) + \gamma m_2 c^2 </math~~> .

	Here ~~<math> E_\text{cm}</math>~~ is ~~the total energy available in the center of mass frame.~~

	~~Using <math> \gamma = \frac{E_1 + m_2 c^2}{E_\text{cm}} </math>, <math> \beta = \frac{p_1 c}{E_1 + m_2 c^2} </math> and~~
	~~<math>p_1^2 c^2 = E_1^2 - m_1^2 c^4 </math> one derives that~~

	~~<math>E_{1,\text{thr}} = \frac{~~(~~m_a c^2+ m_b c^2 + m_c c^2)^2 - m_1^2 c^4 - m_2^2 c^4}{2 m_2 c^2}</math>.~~

	~~== See also ==~~

	* [~~[Threshold displacement energy]]~~

	~~==References==~~
	*http://~~galileo~~.~~phys~~.~~virginia~~.~~edu~~/~~classes~~/~~252~~/~~particle_creation~~.~~html~~

	~~[[Category:Energy (physics~~)]]
	~~[[Category:Particle physics]]~~

en>Toshio Yamaguchi: adding natural number classes navbox

2013-05-30T20:24:35Z

adding natural number classes navbox

← Older revision		Revision as of 22:24, 30 May 2013
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	~~Friends call her Felicidad and her husband doesn~~'~~t like it at all~~. The ~~thing she adores~~ most is ~~flower arranging~~ and ~~she~~ is ~~attempting to make it~~ a ~~profession. Her husband~~ and ~~her chose to reside~~ in ~~Alabama~~. ~~She functions as a financial officer~~ and ~~she will not alter it whenever soon~~.<br><br>~~Feel free~~ to ~~visit my homepage - [http:~~//~~sun~~-~~Lan~~.de/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~14346 sun~~-~~lan~~.de]		In [[particle physics]], the '''threshold energy''' for production of a particle is the minimum [[kinetic energy]] a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle. In most cases, since momentum is also conserved, the threshold energy is significantly greater than the rest energy of the desired particle - and thus there will still be considerable kinetic energy in the final particles.

			==Example==
			Look at the reaction of a proton hitting a stationary proton, <math> p + p \to p + p + \pi^0</math>.

			By going into the center of mass frame, and assuming the outgoing particles have no kinetic energy the conservation of energy equation is:

			<math> E = 2\gamma m_pc^2 = 2 m_pc^2+ m_\pi c^2</math>

			<math> \gamma = \frac{1}{\sqrt{1-\beta^2}} = \frac{2 m_pc^2+ m_\pi c^2}{2 m_pc^2} </math>

			<math> \beta^2 = 1-(\frac{2 m_pc^2}{2 m_pc^2+ m_\pi c^2})^2 \approx 0.13 </math>

			Using relativistic velocity additions:

			<math> v_\text{lab} = \frac{u_\text{cm} + v_\text{cm}}{1+u_\text{cm}v_\text{cm}/c^2} \approx 0.64 c</math>

			So the energy of the proton must be <math> E = \gamma m_p c^2 = \frac{m_p c^2}{\sqrt{1-\beta^2}} = 1221\,</math>MeV.

			== A more general example ==

			Let's look at the case where a particle 1 with lab energy <math>E_1</math> (momentum <math>p_1</math>)
			and mass <math>m_1</math> impinges on a
			target particle 2 at rest in the lab, i.e. with lab energy and mass <math>E_2 = m_2</math>.
			The threshold energy <math>E_{1,\text{thr}}</math> to produce three particles of masses <math>m_a</math>, <math>m_b</math>,
			<math>m_c</math>, i.e.

			<math> 1 + 2 \to a + b + c,</math>

			is then found by asking these three particles to be at rest in the center of mass frame (symbols with
			hat indicate quantities in the center of mass frame):

			<math> E_\text{cm} = m_a c^2+ m_b c^2 + m_c c^2 = \hat{E}_1 + \hat{E}_2 = \gamma (E_1 - \beta p_1 c) + \gamma m_2 c^2 </math> .

			Here <math> E_\text{cm}</math> is the total energy available in the center of mass frame.

			Using <math> \gamma = \frac{E_1 + m_2 c^2}{E_\text{cm}} </math>, <math> \beta = \frac{p_1 c}{E_1 + m_2 c^2} </math> and
			<math>p_1^2 c^2 = E_1^2 - m_1^2 c^4 </math> one derives that

			<math>E_{1,\text{thr}} = \frac{(m_a c^2+ m_b c^2 + m_c c^2)^2 - m_1^2 c^4 - m_2^2 c^4}{2 m_2 c^2}</math>.

			== See also ==

			* [[Threshold displacement energy]]

			==References==
			*http://galileo.phys.virginia.edu/classes/252/particle_creation.html

			[[Category:Energy (physics)]]
			[[Category:Particle physics]]

en>ZéroBot: r2.7.1) (Robot: Adding it:Numero rifattorizzabile

2012-03-14T09:34:57Z

r2.7.1) (Robot: Adding it:Numero rifattorizzabile

New page

Friends call her Felicidad and her husband doesn't like it at all. The thing she adores most is flower arranging and she is attempting to make it a profession. Her husband and her chose to reside in Alabama. She functions as a financial officer and she will not alter it whenever soon.<br><br>Feel free to visit my homepage - [http://sun-Lan.de/index.php?mod=users&action=view&id=14346 sun-lan.de]