<PAGE>


FORM OF WARRANT                                                      Exhibit 4.7


NEITHER THESE SECURITIES NOR THE SECURITIES INTO WHICH THESE SECURITIES ARE
EXERCISABLE HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR
THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM
REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES
ACT"), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN
EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN
AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION
REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE
SECURITIES LAWS AS EVIDENCED BY A WRITTEN LEGAL OPINION OF COUNSEL TO THE
TRANSFEROR TO SUCH EFFECT, THE SUBSTANCE OF WHICH SHALL BE REASONABLY ACCEPTABLE
TO THE COMPANY. THESE SECURITIES AND THE SECURITIES ISSUABLE UPON EXERCISE OF
THESE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR
OTHER LOAN SECURED BY SUCH SECURITIES.

                     AMERICAN SCIENCE AND ENGINEERING, INC.


                                     WARRANT


Warrant No. _____                       Date of Original Issuance:  May 28, 2002

     American Science and Engineering, Inc., a Massachusetts corporation (the
"COMPANY"), hereby certifies that, for value received, _______________________
or its registered assigns (the "HOLDER"), is entitled to purchase from
the Company up to a total of _____________(1) shares of common stock,
$.66 2/3 par value per share (the "COMMON STOCK"), of the Company (each such
share, a "WARRANT SHARE" and all such shares, the "WARRANT SHARES") at an
exercise price equal to $23.52(2) per share (as adjusted from time to time as
provided in SECTION 9, the "EXERCISE PRICE"), at any time and from time to time
from and after the date hereof and through and including May 28, 2007 (the
"EXPIRATION DATE"), and subject to the following terms and conditions. This
Warrant (the "Warrant") is one of a series of similar warrants issued
pursuant to that certain Securities Purchase Agreement, dated as of the date
hereof, by and among the Company and the Purchasers identified therein (the
"Purchase Agreement"). All such warrants are referred to herein,
collectively, as the "Warrants."

--------------------------------------

(1)  Number of shares equal to 25% of the Investment Amount indicated below
     such Purchaser's name on the signature page to the Purchase Agreement,
     divided by the Per Share Price.

(2)  120% of the average of the closing prices for the five consecutive
     Trading Days immediately preceding the Closing Date.

<PAGE>

     1. DEFINITIONS. In addition to the terms defined elsewhere in this Warrant,
capitalized terms that are not otherwise defined herein shall have the meanings
given to such terms in the Purchase Agreement.

     2. REGISTRATION OF WARRANT. The Company shall register this Warrant, upon
records to be maintained by the Company for that purpose (the "WARRANT
REGISTER"), in the name of the record Holder hereof from time to time. The
Company may deem and treat the registered Holder of this Warrant as the absolute
owner hereof for the purpose of any exercise hereof or any distribution to the
Holder, and for all other purposes, absent actual notice to the contrary.

     3. REGISTRATION OF TRANSFERS. The Company shall register the transfer of
any portion of this Warrant in the Warrant Register, upon surrender of this
Warrant, with the Form of Assignment attached hereto duly completed and signed,
to the Company at its address specified herein. Upon any such registration or
transfer, an exchange Warrant to purchase Common Stock, in substantially the
form of this Warrant (any such exchange Warrant, a "NEW WARRANT"), evidencing
the portion of this Warrant so transferred shall be issued to the transferee and
a New Warrant evidencing the remaining portion of this Warrant not so
transferred, if any, shall be issued to the transferring Holder. The acceptance
of the New Warrant by the transferee thereof shall be deemed the acceptance by
such transferee of all of the rights and obligations of a holder of a Warrant.
Warrants and Warrant Shares may only be disposed of in compliance with state and
federal securities laws. In connection with any transfer of Warrant Shares other
than pursuant to an effective registration statement, to the Company, to an
Affiliate of a Holder or in connection with a bona pledge as contemplated in
this Section 3, the Company may require the transferor thereof to provide to the
Company an opinion of counsel selected by the transferor, the form and substance
of which opinion shall be reasonably satisfactory to the Company, to the effect
that such transfer does not require registration under the Securities Act. The
Company acknowledges and agrees that a Holder may from time to time pledge
pursuant to a bona fide margin agreement or grant a security interest in some or
all of the Warrant and Warrant Shares and, if required under the terms of such
arrangement, such Holder may transfer a pledged or secured Warrant and Warrant
Shares to the pledgees or secured parties. Such a pledge or transfer is not
subject to approval of the Company and no legal opinion of the pledgee, secured
party or pledgor shall be required in connection therewith. Further, no notice
shall be required of such pledge.

     4. EXERCISE AND DURATION OF WARRANTS. This Warrant shall be exercisable by
the registered Holder at any time and from time to time on or after the date
hereof to and including 5:00 p.m., New York City time, on the Expiration Date.
At 5:00 p.m., New York City time on the Expiration Date, the portion of this
Warrant available for exercise and not exercised prior thereto shall be and
become void and of no value, provided, that if the closing sales price of the
Common Stock on the Expiration Date is greater than 102% of the Exercise Price
on the Expiration Date, then this Warrant shall be deemed to have been exercised
in full (to the extent not previously exercised) on a "cashless exercise" basis
at 5:00 P.M. New York City time on the Expiration Date; PROVIDED, that if the
registration statement covering the resale of the Warrant Shares is effective on
the Expiration Date, then the Holder shall deliver the Exercise Price for such
Warrant Shares to the Company not later than three Trading Days following the
date on which this Warrant is deemed to have been exercised. The Company may not
call or redeem all or any portion of this Warrant without the prior written
consent of the Holder.


                                      -2-

<PAGE>


     5. DELIVERY OF WARRANT SHARES.

          (a) Upon delivery of this Warrant and the Form of Election to Purchase
to the Company at its address for notice set forth in Section 14 and upon
payment of the Exercise Price multiplied by the number of Warrant Shares that
the Holder intends to purchase hereunder, the Company shall promptly (but in no
event later than three Trading Days after the Date of Exercise (as defined
herein)) issue and deliver to the Holder, a certificate for the Warrant Shares
issuable upon such exercise with any legend required by the Purchase Agreement.
Any Person so designated by the Holder to receive Warrant Shares shall be deemed
to have become holder of record of such Warrant Shares as of the Date of
Exercise of this Warrant. The Company shall, upon request of the Holder, if
available, use its reasonable efforts to deliver Warrant Shares hereunder
electronically through the Depository Trust Corporation or another established
clearing corporation performing similar functions, provided, that, the Company
will not be required to change its transfer agent if its current transfer agent
cannot deliver Warrant Shares electronically through the Depository Trust
Corporation. As used in this Agreement, a "DATE OF EXERCISE" means the date on
which the Holder shall have delivered to the Company (i) the Form of Election to
Purchase attached hereto, appropriately completed and duly signed and (ii)
payment of the Exercise Price for the number of Warrant Shares so indicated by
the Holder to be purchased.

          (b) This Warrant is exercisable, either in its entirety or, from time
to time, for a portion of the number of Warrant Shares. Upon surrender of the
Warrant following one or more partial exercises, the Company shall issue or
cause to be issued, at its expense, a New Warrant evidencing the right to
purchase the remaining Warrant Shares.

          (c) If by the third Trading Day after a Date of Exercise the Company
fails to deliver the required number of Warrant Shares in the manner required
pursuant to Section 5(a), then the Holder will have the right to rescind such
exercise.

          (d) If by the third Trading Day after a Date of Exercise the Company
fails to deliver the required number of Warrant Shares in the manner required
pursuant to Section 5(a), and if after such third Trading Day the Holder
purchases (in an open market transaction or otherwise) shares of Common Stock to
deliver in satisfaction of a sale by the Holder of the Warrant Shares which the
Holder anticipated receiving upon such exercise (a "BUY-IN"), then the Company
shall (1) pay in cash to the Holder the amount by which (x) the Holder's total
purchase price (including brokerage commissions, if any) for the shares of
Common Stock so purchased exceeds (y) the amount obtained by multiplying (A) the
number of Warrant Shares that the Company was required to deliver to the Holder
in connection with the exercise at issue by (B) the closing bid price of the
Common Stock at the time of the obligation giving rise to such purchase
obligation and (2) at the option of the Holder, either reinstate the portion of
the Warrant and equivalent number of Warrant Shares for which such exercise was
not honored or deliver to the Holder the number of shares of Common Stock that
would have been issued had the Company timely complied with its exercise and
delivery obligations hereunder. For example, if the Holder purchases Common
Stock having a total purchase price of $11,000 to cover a Buy-In with respect to
an attempted exercise of shares of Common Stock with a market price on the date
of exercise totaled $10,000, under clause (1) of the immediately preceding
sentence the



                                      -3-
<PAGE>


Company shall be required to pay the Holder $1,000. The Holder shall provide the
Company written notice indicating the amounts payable to the Holder in respect
of the Buy-In.

          (e) The Company's obligations to issue and deliver Warrant Shares in
accordance with the terms hereof are absolute and unconditional, irrespective of
any action or inaction by the Holder to enforce the same, any waiver or consent
with respect to any provision hereof, the recovery of any judgment against any
Person or any action to enforce the same, or any setoff, counterclaim,
recoupment, limitation or termination, or any breach or alleged breach by the
Holder or any other Person of any obligation to the Company or any violation or
alleged violation of law by the Holder or any other Person, and irrespective of
any other circumstance which might otherwise limit such obligation of the
Company to the Holder in connection with the issuance of Warrant Shares. Nothing
herein shall limit a Holder's right to pursue any other remedies available to it
hereunder, at law or in equity including, without limitation, a decree of
specific performance and/or injunctive relief with respect to the Company's
failure to timely deliver certificates representing shares of Common Stock upon
exercise of the Warrant as required pursuant to the terms hereof.

     6. CHARGES, TAXES AND EXPENSES. Issuance and delivery of certificates for
shares of Common Stock upon exercise of this Warrant shall be made without
charge to the Holder for any issue or transfer tax, withholding tax, transfer
agent fee or other incidental tax or expense in respect of the issuance of such
certificates, all of which taxes and expenses shall be paid by the Company;
provided, however, that the Company shall not be required to pay any tax which
may be payable in respect of any transfer involved in the registration of any
certificates for Warrant Shares or Warrants in a name other than that of the
Holder. The Holder shall be responsible for all other tax liability that may
arise as a result of holding or transferring this Warrant or receiving Warrant
Shares upon exercise hereof.

     7. REPLACEMENT OF WARRANT. If this Warrant is mutilated, lost, stolen or
destroyed, the Company shall issue or cause to be issued in exchange and
substitution for and upon cancellation hereof, or in lieu of and substitution
for this Warrant, a New Warrant, but only upon receipt of evidence reasonably
satisfactory to the Company of such loss, theft or destruction and customary and
reasonable indemnity, if requested. Applicants for a New Warrant under such
circumstances shall also comply with such other reasonable regulations and
procedures and pay such other reasonable third-party costs as the Company may
prescribe.

     8. RESERVATION OF WARRANT SHARES. The Company covenants that it will at all
times reserve and keep available out of the aggregate of its authorized but
unissued and otherwise unreserved Common Stock, solely for the purpose of
enabling it to issue Warrant Shares upon exercise of this Warrant as herein
provided, the number of Warrant Shares which are then issuable and deliverable
upon the exercise of this entire Warrant, free from preemptive rights or any
other contingent purchase rights of persons other than the Holder (taking into
account the adjustments and restrictions of SECTION 9). The Company covenants
that all Warrant Shares so issuable and deliverable shall, upon issuance and the
payment of the applicable Exercise Price in accordance with the terms hereof, be
duly and validly authorized, issued and fully paid and nonassessable.



                                      -4-
<PAGE>



     9. CERTAIN ADJUSTMENTS. The Exercise Price and number of Warrant Shares
issuable upon exercise of this Warrant are subject to adjustment from time to
time as set forth in this SECTION 9.

          (a) ADJUSTMENT FOR COMBINATION OR CONSOLIDATION OF COMMON STOCK. If,
at any time while this Warrant is outstanding and after the date of original
issuance, the outstanding shares of the Common Stock shall be combined or
consolidated into a lesser number of shares of Common Stock, the Exercise Price
in effect immediately prior to such combination or consolidation shall,
concurrently with the effectiveness of such combination or consolidation, be
proportionately increased and the number of Warrant Shares issuable upon the
exercise of this Warrant shall be proportionately decreased.

          (b) ADJUSTMENT FOR STOCK DIVIDEND OR SUBDIVISION. If, at any time
while this Warrant is outstanding and after the date of original issuance, the
Company declares or pays any dividend on the Common Stock payable in Common
Stock, or effects a subdivision (by split-up or otherwise) of the outstanding
shares of Common Stock into a greater number of shares of Common Stock, then and
in any such event, the Exercise Price in effect immediately prior to such
subdivision or stock dividend shall, concurrently with the effectiveness of such
stock dividend or subdivision, be proportionately reduced and the number of
Warrant Shares issuable on the exercise of this Warrant shall be proportionately
increased.

          (c) PRO RATA DISTRIBUTIONS. If the Company, at any time while this
Warrant is outstanding, distributes to all holders of Common Stock (i) evidences
of its indebtedness, (ii) any security (other than a distribution of Common
Stock covered by the preceding paragraph), (iii) rights or warrants to subscribe
for or purchase any security, or (iv) any other asset (in each case,
"DISTRIBUTED PROPERTY"), then, at the request of any Holder delivered before the
90th day after the record date fixed for determination of stockholders entitled
to receive such distribution, the Company will deliver to such Holder, within
five Trading Days after such request (or, if later, on the effective date of
such distribution), the Distributed Property that such Holder would have been
entitled to receive in respect of the Warrant Shares for which such Holder's
Warrant could have been exercised immediately prior to such record date. If such
Distributed Property is not delivered to a Holder pursuant to the preceding
sentence, then upon any exercise of the Warrant that occurs after such record
date, such Holder shall be entitled to receive, in addition to the Warrant
Shares otherwise issuable upon such conversion, the Distributed Property that
such Holder would have been entitled to receive in respect of such number of
Warrant Shares had the Holder been the record holder of such Warrant Shares
immediately prior to such record date.

          (d) FUNDAMENTAL TRANSACTIONS. If, at any time while this Warrant is
outstanding: (1) the Company effects any merger or consolidation of the Company
with or into another Person, (2) the Company effects any sale of all or
substantially all of its assets in one or a series of related transactions, (3)
any tender offer or exchange offer (whether by the Company or another Person) is
completed pursuant to which holders of Common Stock are permitted to tender or
exchange their shares for other securities, cash or property, or (4) the Company
effects any reclassification of the Common Stock or any compulsory share
exchange pursuant to which the Common Stock is effectively converted into or
exchanged for other securities, cash or property (in any such case, a
"FUNDAMENTAL TRANSACTION"), then the Holder shall be entitled to exercise this
Warrant pursuant to the terms hereof until the date of the consummation of such


                                      -5-
<PAGE>


Fundamental Transaction (the "TARGET DATE"). The Company shall, no later than
the 20th day immediately preceding the Target Date, deliver a notice to the
Holder (a "COMPANY NOTICE") indicating its intention to either: (1) purchase any
portion of this Warrant which remains unexercised by the Target Date (such
unexercised portion, the "UNEXERCISED WARRANT") for a purchase price, payable in
cash on the Target Date, equal to the Black Scholes value of the Unexercised
Warrant (as calculated by Bloomberg LP) on the Target Date or the date the
Company announces the Fundamental Transaction, whichever is greater or (2) cause
any successor to the Company or surviving entity in such Fundamental Transaction
to promptly issue to the Holder a new warrant substantially in the form of this
Warrant and consistent with the foregoing provisions and evidencing the Holder's
right to purchase the Alternate Consideration (as defined below) for the
aggregate Exercise Price upon exercise thereof (the "NEWCO WARRANT"), PROVIDED,
that if a Company Notice shall evidence an election by the Company to deliver a
Newco Warrant, the Holder shall be entitled by written notice to the Company,
delivered within five (5) Trading Days from its receipt of the Company Notice,
to require the Company to pay to it the Black Scholes amount pursuant to
subclause (1) instead of receiving the Newco Warrant. Notwithstanding the
foregoing, if the Company has not timely delivered either the notice required by
Section 9(h)(ii) or the Company Notice, the Holder shall be entitled to make the
election otherwise available to the Company pursuant to the immediately
preceding sentence. For purpose of this Section, "ALTERNATE CONSIDERATION" shall
mean the securities, cash or property as the Holder would have been entitled to
receive upon the occurrence of a Fundamental Transaction if it had been,
immediately prior to such Fundamental Transaction, the holder of the Warrant
Shares issuable upon exercise in full of this Warrant. The Exercise Price of the
Newco Warrant shall be appropriately adjusted to apply to such Alternate
Consideration based on the amount of Alternate Consideration issuable in respect
of one share of Common Stock in such Fundamental Transaction, and the Company or
its successor or the surviving entity following such Fundamental Transaction
shall apportion the Exercise Price among the Alternate Consideration in a
reasonable manner reflecting the relative value of any different components of
the Alternate Consideration. If holders of Common Stock are given any choice as
to the securities, cash or property to be received in a Fundamental Transaction,
then the Holder shall be given the same choice as to the Alternate Consideration
it receives upon any exercise of this Warrant following such Fundamental
Transaction. The terms of any agreement pursuant to which a Fundamental
Transaction is effected shall include terms requiring any such successor or
surviving entity to comply with the provisions of this paragraph (d) and
ensuring that the Warrant (or any such replacement security) will be similarly
adjusted upon any subsequent transaction analogous to a Fundamental Transaction.

          (e) NUMBER OF WARRANT SHARES. Simultaneously with any adjustment to
the Exercise Price pursuant this Section, the number of Warrant Shares that may
be purchased upon exercise of this Warrant shall be increased or decreased
proportionately, so that after such adjustment the aggregate Exercise Price
payable hereunder for the increased or decreased number of Warrant Shares shall
be the same as the aggregate Exercise Price in effect immediately prior to such
adjustment.

          (f) CALCULATIONS. All calculations under this SECTION 9 shall be made
to the nearest cent or the nearest 1/100th of a share, as applicable. The number
of shares of Common Stock outstanding at any given time shall not include shares
owned or held by or for the account



                                      -6-
<PAGE>


of the Company, and the disposition of any such shares shall be considered an
issue or sale of Common Stock.

          (g) NOTICE OF ADJUSTMENTS. Upon the occurrence of each adjustment
pursuant to this SECTION 9, the Company at its expense will promptly compute
such adjustment in accordance with the terms of this Warrant and prepare a
certificate setting forth such adjustment, including a statement of the adjusted
Exercise Price and adjusted number or type of Warrant Shares or other securities
issuable upon exercise of this Warrant (as applicable), describing the
transactions giving rise to such adjustments and showing in detail the facts
upon which such adjustment is based. Upon written request, the Company will
promptly deliver a copy of each such certificate to the Holder and to the
Company's Transfer Agent.

          (h) NOTICE OF CORPORATE EVENTS. If the Company (i) declares a dividend
or any other distribution of cash, securities or other property in respect of
its Common Stock, including without limitation any granting of rights or
warrants to subscribe for or purchase any capital stock of the Company or any
Subsidiary, (ii) authorizes or approves, enters into any agreement contemplating
or solicits stockholder approval for any Fundamental Transaction or (iii)
authorizes the voluntary dissolution, liquidation or winding up of the affairs
of the Company, then the Company shall deliver to the Holder a notice describing
the material terms and conditions of such transaction, at least 15 calendar days
(and at least 20 calendar days in the case of subclause (ii)) prior to the
applicable record or effective date on which a Person would need to hold Common
Stock in order to participate in or vote with respect to such transaction, and
the Company will take all steps reasonably necessary in order to ensure that the
Holder is given the practical opportunity to exercise this Warrant prior to such
time so as to participate in or vote with respect to such transaction; provided,
however, that the failure to deliver such notice or any defect therein shall not
affect the validity of the corporate action required to be described in such
notice.

     10. PAYMENT OF EXERCISE PRICE. The Holder shall pay the Exercise Price in
one of the following manners:

          (a) CASH EXERCISE. The Holder may deliver immediately available funds;
or

          (b) CASHLESS EXERCISE. At any time after the earlier to occur of the
Effectiveness Date and the Effective Date (each as defined in the Registration
Rights Agreement (as defined in the Purchase Agreement)) when a registration
statement covering the resale of the Warrant Shares and naming the Holder as a
selling stockholder thereunder may not be utilized by the Holders to resell
Warrant Shares, the Holder may surrender this Warrant to the Company together
with a notice of cashless exercise, in which event the Company shall issue to
the Holder the number of Warrant Shares determined as follows:

                 X = Y [(A-B)/A]

     where:

                 X = the number of Warrant Shares to be issued to the Holder.




                                      -7-
<PAGE>



                 Y = the number of Warrant  Shares with  respect to which this
                     Warrant is being exercised.

                 A =  the average of the closing bid prices for the five Trading
                      Days immediately prior to (but not including) the Exercise
                      Date.

                 B = the Exercise Price.

     For purposes of Rule 144 promulgated under the Securities Act, it is
intended, understood and acknowledged that the Warrant Shares issued in a
cashless exercise transaction shall be deemed to have been acquired by the
Holder, and the holding period for the Warrant Shares shall be deemed to have
commenced, on the date this Warrant was originally issued pursuant to the
Purchase Agreement.

     11. LIMITATION ON EXERCISE.

          (a) Notwithstanding anything to the contrary contained herein, the
number of shares of Common Stock that may be acquired by the Holder upon any
exercise of this Warrant (or otherwise in respect hereof) shall be limited to
the extent necessary to ensure that, following such exercise (or other
issuance), the total number of shares of Common Stock then beneficially owned by
such Holder and its Affiliates and any other Persons whose beneficial ownership
of Common Stock would be aggregated with the Holder's for purposes of Section
13(d) of the Exchange Act, does not exceed 4.999% of the total number of issued
and outstanding shares of Common Stock (including for such purpose the shares of
Common Stock issuable upon such exercise). For such purposes, beneficial
ownership shall be determined in accordance with Section 13(d) of the Exchange
Act and the rules and regulations promulgated thereunder. Each delivery of an
Exercise Notice hereunder will constitute a representation by the Holder that it
has evaluated the limitation set forth in this paragraph and determined that
issuance of the full number of Warrant Shares requested in such Exercise Notice
is permitted under this paragraph. By written notice to the Company, the Holder
may waive the provisions of this Section but (i) any such waiver will not be
effective until the 61st day after such notice is delivered to the Company, and
(ii) any such waiver will apply only to the Holder and not to any other holder
of Warrants.

          (b) Notwithstanding anything to the contrary contained herein, the
number of shares of Common Stock that may be acquired by the Holder upon any
exercise of this Warrant (or otherwise in respect hereof) shall be limited to
the extent necessary to ensure that, following such exercise (or other
issuance), the total number of shares of Common Stock then beneficially owned by
such Holder and its Affiliates and any other Persons whose beneficial ownership
of Common Stock would be aggregated with the Holder's for purposes of Section
13(d) of the Exchange Act, does not exceed 9.999% of the total number of issued
and outstanding shares of Common Stock (including for such purpose the shares of
Common Stock issuable upon such exercise). For such purposes, beneficial
ownership shall be determined in accordance with Section 13(d) of the Exchange
Act and the rules and regulations promulgated thereunder. Each delivery of an
Exercise Notice hereunder will constitute a representation by the Holder that it
has evaluated the limitation set forth in this paragraph and determined that
issuance of the full number of Warrant Shares requested in such Exercise Notice
is permitted under this paragraph.



                                      -8-
<PAGE>

This provision shall not restrict the number of shares of Common Stock which a
Holder may receive or beneficially own in order to determine the amount of
securities or other consideration that such Holder may receive in the event of a
merger or other business combination or reclassification involving the Company
as contemplated in Section 9 of this Warrant.

     12. NO FRACTIONAL SHARES. No fractional shares of Warrant Shares will be
issued in connection with any exercise of this Warrant. In lieu of any
fractional shares which would, otherwise be issuable, the Company shall pay cash
equal to the product of such fraction multiplied by the closing price of one
Warrant Share as reported on the Trading Market on the date of exercise.

     13. NO RIGHTS AS SHAREHOLDERS. This Warrant does not entitle the Holder to
any voting rights or other rights as a shareholder of the Company prior to the
exercise of this Warrant and the payment for the Warrant Shares so purchased.

     14. NOTICES. Any and all notices or other communications or deliveries
hereunder (including without limitation any Exercise Notice) shall be in writing
and shall be deemed given and effective on the earliest of (i) the date of
transmission, if such notice or communication is delivered via facsimile at the
facsimile number specified in this Section prior to 5:00 p.m. (New York City
time) on a Trading Day, (ii) the next Trading Day after the date of
transmission, if such notice or communication is delivered via facsimile at the
facsimile number specified in this Section on a day that is not a Trading Day or
later than 5:00 p.m. (New York City time) on any Trading Day, (iii) the Trading
Day following the date of mailing, if sent by nationally recognized overnight
courier service, or (iv) upon actual receipt by the party to whom such notice is
required to be given. The addresses for such communications shall be: (i) if to
the Company, 829 Middlesex Turnpike, Billerica, Massachusetts 01821 Facsimile
No.: (978) 262-8812, Attn: Chief Financial Officer, or (ii) if to the Holder, to
the address or facsimile number appearing on the Warrant Register or such other
address or facsimile number as the Holder may provide to the Company in
accordance with this Section.

     15. WARRANT AGENT. The Company shall serve as warrant agent under this
Warrant. Upon 30 days' notice to the Holder, the Company may appoint a new
warrant agent. Any corporation into which the Company or any new warrant agent
may be merged or any corporation resulting from any consolidation to which the
Company or any new warrant agent shall be a party or any corporation to which
the Company or any new warrant agent transfers substantially all of its
corporate trust or shareholders services business shall be a successor warrant
agent under this Warrant without any further act. Any such successor warrant
agent shall promptly cause notice of its succession as warrant agent to be
mailed (by first class mail, postage prepaid) to the Holder at the Holder's last
address as shown on the Warrant Register.

     16. MISCELLANEOUS.

          (a) This Warrant shall be binding on and inure to the benefit of the
parties hereto and their respective successors and assigns. Subject to the
preceding sentence, nothing in this Warrant shall be construed to give to any
Person other than the Company and the Holder any legal or equitable right,
remedy or cause of action under this Warrant. This Warrant may be


                                      -9-
<PAGE>


amended only in writing signed by the Company and the Holder and their
successors and assigns.

          (b) All questions concerning the construction, validity, enforcement
and interpretation of this Agreement shall be governed by and construed and
enforced in accordance with the internal laws of the State of New York, without
regard to the principles of conflicts of law thereof. Each party agrees that all
legal proceedings concerning the interpretation, enforcement and defense of the
transactions contemplated by this Warrant (whether brought against a party
hereto or its respective affiliates, directors, officers, shareholders,
employees or agents) (each, a "PROCEEDING") shall be exclusively commenced in
the state and federal courts sitting in the City of New York, Borough of
Manhattan (the "NEW YORK COURTS"). Each party hereto hereby irrevocably submits
to the exclusive jurisdiction of the New York Courts for any Proceeding, and
hereby irrevocably waives, and agrees not to assert in any Proceeding, any claim
that it is not personally subject to the jurisdiction of any such court, or such
New York Courts are improper or inconvenient venue for such proceeding. Each
party hereby irrevocably waives personal service of process and consents to
process being served in any Proceeding by mailing a copy thereof via registered
or certified mail or overnight delivery (with evidence of delivery) to such
party at the address in effect for notices to it under this Warrant and agrees
that such service shall constitute good and sufficient service of process and
notice thereof. Nothing contained herein shall be deemed to limit in any way any
right to serve process in any manner permitted by law. Each of the Company and
the Holder hereby irrevocably waives, to the fullest extent permitted by
applicable law, any and all right to trial by jury in any Proceeding. If any
party shall commence an action or proceeding to enforce any provisions of this
Warrant, then the prevailing party in such Proceeding shall be reimbursed by the
other party for its reasonable attorneys' fees and other reasonable costs and
expenses incurred with such Proceeding.

          (c) The headings herein are for convenience only, do not constitute a
part of this Warrant and shall not be deemed to limit or affect any of the
provisions hereof.

          (d) In case any one or more of the provisions of this Warrant shall be
invalid or unenforceable in any respect, the validity and enforceability of the
remaining terms and provisions of this Warrant shall not in any way be affected
or impaired thereby and the parties will attempt in good faith to agree upon a
valid and enforceable provision which shall be a commercially reasonable
substitute therefor, and upon so agreeing, shall incorporate such substitute
provision in this Warrant.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK,
                             SIGNATURE PAGE FOLLOWS]




                                      -10-
<PAGE>


         IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed by its authorized officer as of the date first indicated above.

                           AMERICAN SCIENCE AND ENGINEERING, INC

                           By:
                              -----------------------------------------
                           Name:
                                ---------------------------------------
                           Title:
                                 --------------------------------------



                                      -11-
<PAGE>


                          FORM OF ELECTION TO PURCHASE

                    To American Science and Engineering, Inc:

     In accordance with the Warrant enclosed with this Form of Election to
Purchase, the undersigned hereby irrevocably elects to purchase _____________
shares of common stock ("COMMON STOCK"), $.66 2/3 par value per share, of
American Science and Engineering, Inc. and, if such Holder is not utilizing
the cashless exercise provisions set forth in this Warrant, encloses herewith
$________ in cash, certified or official bank check or checks or other
immediately available funds, which sum represents the aggregate Exercise
Price (as defined in the Warrant) for the number of shares of Common Stock to
which this Form of Election to Purchase relates.

     By its delivery of this Form of Election To Purchase, the Holder represents
and warrants to the Company that in giving effect to the exercise evidenced
hereby the Holder will not beneficially own in excess of the number of shares of
Common Stock (determined in accordance with Section 13(d) of the Securities
Exchange Act of 1934) permitted to be owned under Section 11 of this Warrant to
which this notice relates.

     The undersigned requests that certificates for the shares of Common Stock
issuable upon this exercise be issued in the name of


                                          PLEASE INSERT SOCIAL SECURITY OR
                                          TAX IDENTIFICATION NUMBER



<PAGE>


                               FORM OF ASSIGNMENT

           [To be completed and signed only upon transfer of Warrant]

     FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ________________________________ the right represented by the within
Warrant to purchase ____________ shares of Common Stock of American Science and
Engineering, Inc. to which the within Warrant relates and appoints
________________ attorney to transfer said right on the books of American
Science and Engineering, Inc. with full power of substitution in the premises.

Dated: _______________, ____


                                    ---------------------------------------
                                    (Signature must conform in all respects
                                     to name of holder as specified on the face
                                     of the Warrant)



                                    ---------------------------------------
                                    Address of Transferee



                                    ---------------------------------------

                                    ---------------------------------------


In the presence of:


--------------------------